By developing the previously proposed method of combining continuum mechanics with Einstein Field Equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangian density equal to the invariant of the electromagnetic field was obtained, vanishing four-divergence of canonical four-momentum appears to be consequence of the Poyinting theorem, and explicit form of one of gauges of the electromagnetic four-potential was introduced. The proposed method allows for further development with additional fields.

In this paper, we examine the weak deflection angle and greybody factor of magnetized regular black hole. We implement the Gauss-Bonnet theorem on magnetized regular black hole to get the deflection angle. Moreover, we analyze the influence of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. We observe the graphical behaviour of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. Lastly, we study the rigorous bound phenomenon of the greybody factor of magnetized regular black hole. For this purpose we calculate greybody factor results and analyze the graphical behaviour of greybody bound for the different values of the parameters.

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translate into a gradient expansion that, at the leading order, can recover the BKL solution. We solve exactly the leading order equations in a spherical symmetric case and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

We propose that the Big Bang does not have a singular start, but that it originates from gravitational collapse of a low density cloud that collapsed 25 Gyrs ago to form a Black Hole (BH) of mass M ≃ 6 × 1022M⊙. The collapse continued inside the BH for 11Gyrs until the density achieves neutron degeneracy and the collapse bounces into expansion like a core collapse supernova. From observations today, this model is very similar to the standard Big Bang cosmology but there is no need for Inflation or Dark Energy (DE). The observed cosmological constant Λ is not a new form of DE, but results from the dynamics of the Big Bang expansion inside the BH event horizon rS = 2GM = √3/Λ. Why our Universe has such a large mass M (or small Λ value)? If τO(≃ 10Gyr) is the astronomical timescale needed for observers like us to exist, we find a simple anthropic prediction, based only on gravitational collapse from Gaussian fluctuations, that the maximum probability for M is MO < M < 3MO where MO = τO/3G. This agrees well with the measured values for τO and M in our Universe.

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

We received an Honorable Mention at the Gravity Research Foundation 2018 Awards for Essays on Gravitation by showing that a correct general relativistic interpretation of the Mössbauer rotor experiment represents a new, strong and independent, proof of Einstein's general theory relativity (GTR). Here we correct a mistake which was present in our previous computations on this important issue by deriving a rigorous computation of the additional effect of clock synchronization. Finally, we show that some recent criticisms on our general relativistic approach to the Mössbauer rotor experiment are incorrect, by ultimately confirming our important result.

In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and also suggest a rapid expansion of the matter density, thus making mechanism such as inflation (which demands invoking and ad-hoc scalar field) redundant. This is in accordance with Occam’s razor.

The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lema\^itre-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations.

In this work, we study the existence of strange star in the background of f(T,T) gravity in the Einstein spacetime geometry, where T is the torsion tensor and T is the trace of the energy-momentum tensor. The equations of motion are derived for anisotropic pressure within the spherically symmetric strange star. We explore the physical features like energy conditions, mass-radius relations, modified TOV equations, principal of causality, adiabatic index, redshift and stability analysis of our model. These features are realistic and appealing to further investigation of properties of compact objects in f(T,T) gravity as well as their observational signatures.

Difference in two quantum states defined for a point in space time is represented by space time curvature and the superposition of these quantum states will affect the momentum of mass existed at that point. Analogy of the same with Einstein’s General relativity field equation and Einstein’s gravitational constant , indicated an equation containing ‘Hubble’s constant H , Einstein’s gravitational constant ‘H’ and Siva’s constant ‘K’. Its output is a quadratic equation. Solution to this quadratic equation predicted a fundamental force particle. This solution gives the diameter of that particle. From the fundamental principles, the diameter of this force particle gives the coupling constant of that fundamental force. Prediction and review of this particle may provide us new insights in to quantum physics and standard model of particle physics. From the first principles, it is discussed that this particle can be claimed as a force carrying particle of a fundamental force related to dark matter. This work has provided simple explanation to reconcile quantum nature of space time with smooth space time of General Relativity. This has demanded the necessity to introduce a new postulate in quantum mechanics which is beyond Hilbert space and Dirac notation. A new perspective of uncertainty principle in quantum mechanics has been elaborated.

In this work, we try to find a way to describe the physical law of micro-world under the frame of a space-time theory. By introducing the scalar fields $\mathcal{D}\left( x\right)$ and $\zeta\left( x\right) $, we rewrite the action of conventional field theory and the Lagrangian describing the motion of the particle, where a modified space-time relation is obtained. To test the correctness of this attempt, we demonstrate the Klein-Gordon equation by the Hamilton-Jacobi method in four dimensional form and present a time delay for the ground state of hydrogen atom.

We present a geometric field theory in which the action and field equation are constructed from an ultra-high-density vector field and its covariant derivative and have full general covariance in a higher-dimensional spacetime. The field equation is the simplest possible generalisation of the Poisson equation for gravity consistent with general covariance and the equivalence principle. It contains the Ricci tensor and metric acting as operators on the vector field. If the covariant derivative is diagonalisable across a neighbourhood under real changes of coordinate basis, spacetime coincides with a product manifold. The dimensionalities of the factor spaces are determined by its eigenvalues and hence by its algebraic invariants. Tensors decompose into multiplets which have both Lorentz and internal symmetry indices. The field equation has a `classical vacuum' solution which is a product of Minkowski spacetime and an Einstein manifold. A worked example is provided in six dimensions. Away from this classical vacuum, connection components in appropriate coordinates include $SO(N)$ gauge fields. The Riemann tensor includes their field strength. Unitary gauge symmetries act indirectly on tensor fields and some or all of the unitary gauge fields are found amongst the $SO(N)$ gauge fields. Symmetry restoration occurs at the zero-curvature `decompactification limit', in which all dimensions appear on the same footing.

Considered is “time as an interval” including time from the past and from the future, in contrast to time as a moment. Equilibrium as the basis for a description of changing properties in physics is understood to depend on the “mean velocity theorem”, while a “time” of equilibrium resembles a center of weight. This turns out to be a good method to derive properties for any function of time t including space coordinates q(t) and expressions for the time dependent Hamiltonian. Introduced are derivatives depending on time intervals instead of time moments and with these a new relation between the Lagrangian L and the Hamiltonian H. As an application introduced is a step by step method to integrate stationary state “local” time interval measurements to beyond “locality” in General Relativity. Because of limits on the measures of the resulting time intervals and their asymmetry, this allows for a probabilistic interpretation of quantities that have these intervals as time domain in QM. Their asymmetry also questions the time reversal symmetry of GR. Another application of time intervals is the discussion of the measurement of starlight radiation energy and QM wave packet collapse as an example of a time dependent Hamiltonian. Finally a relation between starlight frequency, metric and space- and time intervals is found. Discussed is how finite and asymmetric time intervals correspond to time dependent H and symmetric infinite time intervals to a time independent H. From there, in cosmological perspective, finite time intervals can help to describe how entropy change could relate to dark energy.

In this work, we examine the deflection angle of black hole in effective loop quantum gravity in non-plasma medium via the geometrical technique of Gibbons and Werner in weak field limits. For this, we attain the optical metric and calculate the Gaussian optical curvature and then we apply the Gauss-Bonnet theorem. We also study the influence of the plasma and dark matter mediums on the deflection angle. Further, we obtain the deflection angle by using Keeton and Petters method. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the bending angle and bounds on the greybody factor. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduces to the Schwarzschild black hole solutions when dimensionless non-negative parameter $A_{\lambda}=0$.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. It allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. Using Hamilton’s principle we transform the differential equation relativistically into an integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by the rotations of real particle field geometries in Minkowski space. Because the properties of energy are universal the same equations are then used to describe the field geometry of galaxies despite vast differences in lifetime. They reveal a symmetry between the electromagnetic fields of atoms and the gravitational fields of galaxies due to similarities in the exchange of energy by radial and transverse fields. Our analysis reveals that the conjugate variables energy and time permit differences between atomic and galactic structure to be compared in a more intuitive way than by means of the differential equations of motion which use the conjugate variables position and momentum.

The general theory of relativity (GR) is known to be invariant under smooth coordinate transformations (diffeomorphism). This group has a subgroup known as the Lorentz group of symmetry which is manifested in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.

The Universe has a gravitational horizon with a radius R_h = c/H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaitre-Robertson-Walker spacetime, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model R_h = ct. As of today, this cosmology has passed over 20 observational tests, often better than LCDM. The gravitational radius R_h therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to mc². This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches R_h. In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.

In this paper a high-power and propellant-free electromagnetic propulsion is proposed based on the General Relativity and nuclear fusion technology. We find that Riemann curvature vanish and geodesic motion is free from gravitational field locally in a special space-time, which demonstrates the feasibility of propellant-free electromagnetic propulsion. To achieve high-power propulsion in Schwarzschild background, we choose current loop as axisymmetric field source and obtain exact solution of Einstein-Maxwell field equation using Killing symmetry and Ernst generation technique. An implementation with superconductor shield is given according to the Meissner effect, calculation implies that the device can be sufficiently free from gravitational field with the aid of existing nuclear fusion engineering.

We explore the deflection angle in the framework of improved Schwarzschild Black hole utilizing the most advance geometrical path adopted by Gibbon-Werner. To investigate deflection angle of the photon ray by weak gravitational lensing for this black hole, we derive the optical curvature and perform the application of Gauss-Bonnet theorem on the optical metric. Moreover, we study the impacts of the plasma medium in context of the weak gravitational lensing in relate to this black hole. Further, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Also, we find the rigorous bound base upon the greybody factor for improved Schwarzschild black hole. A while later, we contrast our conclusions about deflection angle with the deflection angles of Schwarzschild black hole within plasma and non-plasma mediums.

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

Through a brief analysis of the basic principle of relativity, it is found that there is a contradiction in principle between general relativity and special relativity in solving the specific problem of the clock moving around the earth, and one of them must be wrong. Through comparative analysis of five physical phenomena and experiments, it is proved that there are serious problems in the space concept of relativity theory and classical physic. At the same time, the different concept of absolute airspace is further expounded and demonstrated, and the related space-time physical phenomena and experiments are perfectly explained by this concept. According to this idea, a new time transformation relation is deduced and its correctness is demonstrated. It is proved that the principle of special relativity and special relativity are wrong, and a series of physical laws and physical explanations generated by special relativity may also be wrong, and a series of amendments or new interpretations need to be made.

The standard Cosmological model (LCDM) assumes that the expanding spacetime around us is infinite, which is inconsistent with the observed cosmic acceleration unless we include Dark Energy (DE) or a Cosmological Constant ($\Lambda$). But the observed cosmic expansion can also be explained with a finite mass $M$, inside a uniform expanding sphere, with empty space outside. An object with mass $M$ has a gravitation radius $r_S=2GM$. When $M$ is all contained within $r_S$, this is a Black Hole (BH). Nothing can escape from $r_S$, which becomes a boundary for the inside dynamics. In the limit where there is nothing outside, the inside corresponds to a local isolated Universe. The $r_S$ boundary condition corresponds to an effective force which is mathematically equivalent to $\Lambda=3/r_S^2$. We can therefore interpret cosmic acceleration as a measurement of the gravitational boundary of our Universe, with a mass $M = \frac{c^2}{2G}\sqrt{3/\Lambda} \simeq 6 \times 10^{22} M_{\odot}$. Such BH Universe (BHU) is observationally very similar to the LCDM, except for the very large scale perturbations, which are bounded by $r_S$.

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

In Einstein’s Special Relativity(SR), time is treated as one of the four dimensions within spacetime and is relative in nature. Typically, a photon clock serves as the illustrative device in the time dilation thought experiment, featuring a single photon bouncing between two mirrors. However, the present paper identifies a fundamental flaw in this thought experiment, hence challenging its validity. Contrary to SR, this paper asserts that time is a consequence of motion. Space and time should be treated differently as proposed by classical mechanics. Importantly, this stance does not challenge the concept of curved space in General Relativity (GR), but rather questions the idea of relative time, as employed in both SR and GR. The absence of time dilation also dispels the twin paradox, prompting a necessary reassessment of the second postulate of relativity to ensure a more precise depiction of relativistic effects.

In this paper, first we use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural explanation for the famous, more than a century old, 4/3 factor in the electromagnetic mass.

Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

The exceptional Jordan algebra is the algebra of $3 \times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan’s algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new U(1) gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

Recent advances in understanding the Planck scale have led to a new, straightforward method for quantizing the general theory of relativity. This results in a theory of gravity that predicts the same outcomes as general relativity with greater fundamental comprehension connected directly to the Planck scale.

In this paper, the Hafele‐Keating experiment and the geostationary orbit satellite of related physics problems of are analyzed and discussed in detail. If researchers read the paper and think about it, It will be found that the Hafele‐Keating experiment and the geostationary satellite problem prove that some of the core ideas and theories of relativity are seriously wrong. Isnʹt that a very serious problem in physics? Canʹt this cause the academic circles to pay great attention to it? Isnʹt this worthy of in‐depth analysis and research? The core of the paper is to point out that there are problems with the space concept and the reference system theory of classical physics and relativity, And that would bring up a whole host of physics problems. It takes a concerted effort from the academic community, Do furtherin‐depth analysis and research. Strive forthe further discovery and perfection of physics theory.

In classical General Relativity, White Holes (WH) refer to the time reverse Schwarzschild (SW) Black Hole (BH) solution of a point mass $M$ and gravitational radius $r_S=2GM$. The SW metric is static so that a time reverse WH solution simply corresponds to a violation of causality. The WH solution does not make any physical sense here. For a more physical model, such as the Lemaitre-Tolman-Bondi (LTB) metric with finite mass inside $r_S$, we show that both the expanding and collapsing solutions correspond to a BH and not to a WH.

In the present paper we investigate the conservative conditions in Quadratic Gravity. It is shown explicitly that the Bianchi identities lead to the conservative condition of the left-hand-side of the (gravitational) field equation. Therefore, the total energy-momentum tensor is conservative in the bulk (like in General Relativity). However, in Quadratic Gravity it is possible to have singular hupersurfaces separating the bulk regions with different behavior of the matter energy-momentum tensor or different vacua. They require special consideration. We derived the conservative conditions on such singular hypersurfaces and demonstrated the very possibility of the matter creation. In the remaining part of the paper we considered some applications illustrating the obtained results.

This paper presents research within the topic of special relativity. First, we show that time dilation and length contraction do not necessarily require that the speed of light be the same in all reference frames. It is only necessary to require that the speed of light be finite in any particular frame. Next, we demonstrate that the relativistic Doppler shift for electromagnetic waves has an analogue for extended material objects, and furnish an expression for the relative velocity of such objects in terms of what we call their "rest length shift''. An alternative velocity, which we call "rest velocity'', is then introduced to simplify the Lorentz transformation formulas. We also show that regular velocity can be regarded as the geometric average of the "rest velocity'' and another type of velocity we term "contracted velocity". We conclude by formulating the relationship between regular and "rest'' velocity for non-uniform motion in one, two, and three dimensions.

In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss-Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behaviour of the bending angle ψ with respect to the impact parameter b, mass m as integration constant and parameter q in non-plasma and plasma mediums. We examine that deflection angle is exponentially increasing as direct with charge. Also, we observe that for small values of b, ψ increases and for large values of b the angle deceases. We also considered an analysis to the shadow cast of the wormhole relative to an observer at various locations. Comparing it the the Schwarzschild shadow, shadow cast is possible for wormhole as r<2m. At r>2m, the Schwarzschild is larger. As r → ∞, we have seen that the behavior of the shadow, as well as the weak deflection angle, approaches that of the Schwarzschild black hole. Overall, the effect of plasma tends to decrease the value of the observables due to the wormhole geometry.

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

Abstract: A new method for constructing exact solutions of the General Relativity equations for a dusty matter with fractal property is proposed. This method allows to find the solution of the GR-equations in terms of matter velocities : the connection coefficients and the Ricci tensor of space-time are expressed in terms of matter velocities; the metric tensor and the matter density are found as functions of velocity from the GR-equations. The connection coefficients and the Ricci tensor are invariant with respect to the discrete scaling transformation of velocity , where is constant. Therefore, the found solution can be used to simulate the fractal properties of the cosmic web in terms of matter velocities. This solution includes isotropic and anisotropic distributions of matter density. In an isotropic case, there is a class of exact solutions including both the well-known Friedmann’s solution and a solution with a periodic distribution of the matter density in space. This last solution may be used to simulate the quasi-periodic distribution of matter in the cosmic web. It is possible that, the cosmic web and its fractal properties are the space-time primary properties. These properties are described with a deformation tensor of the space-time.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

In this work, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss-Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss-Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of NLED, plasma, and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

Nonlinear electrodynamics is known as the generalizations of Maxwell electrodynamics at strong fields and presents interesting features such as curing the classical divergences present in the linear theory when coupled to general relativity. In this paper, we consider the asymptotically flat Reissner-Nordstr\"om black hole solution with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic charge parameters on the black hole, viz. weak deflection angle of photons and massive particles using Gauss-bonnet theorem. Moreover, we apply the Keeton-Petters formalism to confirm our results of the weak deflection angle. Apart from vacuum, their influence in the presence of different media such as plasma and dark matter are probed as well. Finally, We examine the black hole shadow cast using the null-geodesics method and investigate its spherically in-falling thin accretion disk. Our inferences show how the magnetic charge parameter $p$ affects the other physical quantities; so, we impose some constraints on this parameter using the observations from the Event Horizon Telescope.

Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

This interdisciplinary work presents a novel patent pending method of inertial electrostatic confinement (IEC) fusion called the Nuclear Electromagnetic Shaping Accelerator Reactor (NESAR) that addresses all of the major failure problems with currently known methods of IEC fusion. A brief background of previous IEC methods that generate a negative potential well to accelerate ions for fusion will be reviewed and compared to the NESAR method of magnetic confinement. In addition, a direct comparison will be presented between the NESAR and the tokamak method of fusion. The NESAR method of fusion obtains the plasma oscillation and compression capabilities of a tokamak without producing the catastrophic magnetic reconnection disruptions that currently plague tokamaks. Since the NESAR can oscillate charged particles comparable to the tokamak, this work will briefly review the history of the tokamak, how sawtooth magnetic reconnection occurs, and how the NESAR precludes the occurrence of magnetic reconnection. This work will also review the beginnings of a novel unified field theory that has obtained interest from the Defense Advanced Research Projects Agency (DARPA). This unified field theory is based upon the trajectory of charged particle movements within the NESAR, which is the only concept of magnetic confinement in the world that may allow charge particles to collectively interact relatively to a solitary location. Due to this possible capability, the confined charged particles have the potential to experience curved trajectories; allowing for the effects of curvature deviation to be placed upon the charged particle within the magnetic confines of the NESAR. If charged particles can experience curvature deviation then deviated acceleration is generated; allowing the electromagnet field to be propelled to a higher spatial dimension that could influence spacetime. Finally, this work will review another theory that explains how magnetic pole reversals are observed by the National Aeronautics and Space Administration’s (NASA) coiled magnetic field detectors. This theory requires little to no postulations to be framed and it is purely based upon the trajectory of charged particles within the NESAR, Michael Faraday’s law of induction, and experimental observations of rotating plasmas.

On a rotating disk, two particles bounce at the vertices of a regular polygon in opposite directions. On the return to the entry point, a clock measures the time difference, called Sagnac effect. Due to Coriolis effects, the counterclockwise and clockwise paths are different. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The existence of a transition between a classical and a relativistic regime is proved. An experimental verification is proposed. Although the two Sagnac effects seem analogous, in detail their behavior is quite different.

The geodesics on a relativistic manifold are given by the well-known equation involving the Christoffel coefficients. This equation can be solved numerically step by step and transposed into a quantization. We study here the effect of this quantization on the Schwarzschild spacetime, more precisely in the Kruskal-Szekeres map.

The mission here is to see if we can find bound states for tachyons in some gravitational environment. That could provide an explanation for the phenomena called Dark Matter. Starting with the standard Schwarzschild metric in General Relativity, which is for a static and spherically symmetric source, it appears unlikely that such localized orbits exist. In this work the usual assumption of isotropic pressure is replaced by a model that has different pressures in the radial and angular directions. This should be relevant to the study of neutrinos, especially if they are tachyons, in cosmological models. We do find an arrangement that allows bound orbits for tachyons in a galaxy. This is a qualitative breakthrough. Then we go on to estimate the numbers involved and find that we do have a fair quantitative fit to the experimental data on the Galaxy Rotation Curve. Additionally we are led to look in the neighborhood of a Black Hole and there we find novel orbits for tachyons.

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life's origin. Non-biological and biological entities obey the universal laws of nature grounded on space-time symmetry (STS) transformations. The fabric of STS is the immense subject of our review. The symmetry, encompassing behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. Objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation - mirror reflection. Chirality as a symmetry element reflecting the property of asymmetry (or dissymmetry) is the critical structural feature of natural systems, including sub-atomic particles and living matter. The inheritance of molecular symmetry from the symmetry of elementary particles points to the bi-directional causal pathway of prevalent bio-chirality. We assume that both extremities of spatial dimension naturally influence this transitional state of biological matter. The current review promotes an integrative holistic approach to the new experimental results in fast-developing and divergent branches of STS and biological chirality. The generalized view on biological chirality is a necessary and promising avenue for adequately understanding the link between protein folding, cell morphology, neuronal signaling, and laterality of cognitive functions.

On the basis of the findings of this paper, the theories of quantum mechanics and general relativity can be expressed in a comprehensive theory. The events were surveyed length of the time, in the Euclidean six-dimensional space-time (R6=x1+x2+x3+t1+t2+t3). Previous studies have not studied the relationship between the origin of matter's inherent properties, fundamental constants, and quantum mechanics phenomenon with space-time geometry. This theory prediction the with certainty obtained probabilistic results of quantum mechanics. This prediction is on the basis of metric resulting from the Eccentricity of the Ellipse due to the object density, in the length of time. The cause and nature of dark matter and dark energy are the findings of this article.

The conventional measure of cosmic acceleration, denoted as \( q \), relies heavily on the frame of reference and operates within a 3D space-like coordinate system, potentially leading to misinterpretations of underlying physics. In this study, we propose a novel measure, \( q_E \), grounded in distances between causal events in 4D null space. We compare \( q_E \) with the standard \( q \) using observational data from supernovae (SN) and radial galaxy/quasar (QSO) clustering (BAO) to find a better alignment of data with \( q_E \). Our analysis indicates that cosmic expansion, when viewed in the rest frame, is decelerating, with events confined by an Event Horizon akin to that of a Black Hole interior. Rather than invoking new dark energy or modified gravity, we propose that \( \Lambda \) corresponds to a boundary term exerting an attractive influence, analogous to a rubber band resisting further expansion and preventing horizon crossing of events. Contrary to prevailing notions, interpreting current cosmic expansion measurements as deceleration, rather than acceleration, offers a more accurate depiction of observed phenomena and the underlying physics. This reevaluation prompts further investigation into the nature of cosmic expansion, as well as the exploration of alternative frameworks and measures in cosmology.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

The identification of fetal cells in the blood and tissues of healthy mothers raised questions about the potential alloreactive origins of various diseases, such as autoimmunity, diabetes, arteriosclerosis, and cancer. However, the extent to which alloreactivity contributes to these diseases remains unverified. This study presents a basic mathematical disease model based on the genes’ origin and immunological interactions. This model, grounded in set theory, classifies these immunological interactions based on their intrinsic, extrinsic, and allogeneic nature. Therefore, this model offers an unexpected common theoretical foundation for understanding alloreactivity, genetic diseases, and infections. Furthermore, this model provides a valuable framework for scrutinizing the role of alloreactivity in health and disease.

In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. A preliminary analysis of this option denoted "nano relativistic scale" is studied in the current paper.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

In paper I, we showed that the observed (LCDM) Universe can be modeled as a local Black Hole (BH) Universe (BHU) of fixed mass M, without Dark Energy (DE): cosmic acceleration is caused by the BH event horizon rS=2GM. %The same BHU solution can be used to model the interior of a stellar or galactic BHs. Here, we propose that our BHU could form from the hierarchical free-fall collapse of regular matter. We argue that the singularity could be avoided with a Big Bounce explosion, caused by neutron degeneracy pressure (Pauli exclusion principle). This happens at GeV energies, like in core collapse supernova, well before the collapse reaches Planck energies (1E19 GeV). If our universe formed this way, there is no need for cosmic Inflation or a singular start (The Big Bang). Nucleosynthesis and recombination follow a hot expansion, like in LCDM, but cosmological measurements, which are free parameters in LCDM, could be estimated from first principles. Dark Matter could be made up of a wide mass range of primordial compact objects (BHs and Neutron stars), remnants of the collapse and bounce, which can provide a faster start for galaxy formation. We present a simple prediction to explain the observed value of Lambda and the coincidence problem.

This paper examines radially infalling worldlines in both Schwarzschild and Kruskal-Szekeres coordinates. A new Schwarzschild coordinate chart is presented which emphasizes the curvature of both the time and space coordinates and makes clear not only the mechanism by which the inertial observer is accelerated relative to the rest observers, but also clearly shows the light-like nature of the inertial worldline at the event horizon. The light-like nature of the falling frame is then supported by examining the falling worldlines in Kruskal-Szekeres coordinates. The effect of length contraction in the falling frame is also analyzed in both Schwarzschild and Kruskal-Szekeres coordinates.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

In previous works we have developed the concept of a relativistic engine taking into account the phenomena of retardation of electromagnetic fields. We have shown that Newton’n third law cannot strictly hold in a distributed system, where the different parts are at a finite distance from each other and thus force imbalance is created at the system’s center of mass. As the system is affected by a total force for a finite period, mechanical momentum and energy are acquired by the system. In previous works we relied on the fact that the bodies were macroscopically natural. Lately we relaxed this assumption and studied charged bodies, thus analyzing the consequences on a possible electric relativistic engine. On the first paper on this subject we investigated this phenomena in general but gave an example of a system only at the stage of reaching a stationary state, a second paper was devoted to the same but on the atomic scale, here we shall analyze the charge relativistic engine in a general time dependent setting.

In physics, thought experiments are impressive heuristic tools. They are valuable instruments to help scientists find new results and to teach students the known ones. However, as we shall show, they should always be received with prudence, even when they are a shortcut to 'prove' well-established results. Here, we show that the most widely known thought experiments devised to derive the gravitational frequency shift from energy conservation are, in fact, problematic. When properly set and correctly read, those thought experiments reveal that the existence of the gravitational frequency shift is, in fact, at odds with energy conservation. We also propose two new simple thought experiments, one using the conservation of energy and the other the conservation of linear momentum, that corroborate that conclusion, showing that those conservation principles do not imply the gravitational frequency shift. We think that our results may be of some epistemological interest and could serve as a warning sign on how thought experiments should be received and trusted.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

This paper is devoted to study the gravitational lensing for Curvature-coupled antisymmetric wormhole solution to compute the bending angle of light by utilizing the Gibbons and Werner technique. To achieve this, we find the Gaussian optical curvature and then apply Gauss-Bonnet theorem in the weak field limits. We also study the effects of plasma as well as dark matter mediums on the bending angle. Moreover, we analyze the graphical behaviour of the deflection angle $\alpha$ with respect to the impact parameter $\sigma$ and minimal radius $r_{0}$ in non-plasma and plasma mediums. We examine that deflection angle shows direct relation with $r_{0}$ such that large values of $r_{0}$ gives large deflection angle and small values of $r_{0}$ gives small deflection angle. For impact parameter $\sigma$, deflection angle $\alpha$ shows inverse relation. Additionally, we derive the deflection angle of light by using Keeton and Petters method and compare with the previous results.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

In this work, the conceptions of the electrodynamics of action-at-a-distance and of electromagnetic fields are reviewed and confronted, with the aim of clarifying whether it is possible to propose a Weberian theory of action-at-a-distance, which together with a renewed mechanics (both re-specting the existence of a limiting velocity c) could constitute a framework capable of yielding predictions equivalent to those of the conventional Maxwell-Lorentz and SRT framework. In this work, it is shown that, considering basic assumptions about the interaction process, understanding it as an action exchange process, it is possible to derive the expression of the electrodynamic Phipps’ potential energy between two interacting charges. It is also shown that, with the same assumptions and the additional hypothesis that the interaction is supported by a mediating agent (aether or field) which is perturbed by the transmission of action, this perturbation obeys the wave equation (one of the main drawbacks of Weberian electrodynamics). Another aim of the work is to confront the relational electrodynamic formulations (supported by Galilean transformations that assume a universal time) with the Maxwell-Lorentz formulation of electromagnetism (linked to Lorentz transformations that entail local times), in order to elucidate whether the space-time to which the SRT leads us is a mere mathematical artifice or an inescapable reality.

This paper is devoted to compute the weak deflection angle for Kalb-Ramond traversable wormhole solution in plasma and dark matter mediums by using the method of Gibbons and Werner. To acquire our results, we evaluate Gaussian optical curvature by utilizing the Gauss-Bonnet theorem in the weak field limits. We also investigate the graphical influence of deflection angle $\tilde{\alpha}$ with respect to the impact parameter $\sigma$ and minimal radius $r_0$ in plasma medium. Moreover, we derive the deflection angle by using different method known as Keeton and Petters method. We also examine that if we remove the effects of plasma and dark matter, the results become identical to that of non-plasma case.

In this paper, we investigate an exact Universe which is observational viable and filled with binary mixture of perfect fluid and cosmological constant $\Lambda$. Owning the non-uniform expansion of cosmos, we have considered redshift drift $\dot{z} = -(1+z)H_{0}+H(z)$ and performed statistical test to obtain the best fit value of model parameters of derived Universe with its observed values. Here $H_{0}$ and $z$ denote the present value of Hubble constant and redshift respectively. We estimate the best fit values of Hubble constant and density parameters are $H_{0} = 68.58 \pm 0.84$ km/s/Mpc, $(\Omega_{m})_{0} = 0.26 \pm 0.010$ and $(\Omega_{\Lambda})_{0} = 0.71 \pm 0.025$ by bounding the derived model with latest observational Hubble data (OHD) while with joint Pantheon data and OHD, its values are $H_{0} = 71.93 \pm 0.58$ km/s/Mpc, $(\Omega_{m})_{0} = 0.272 \pm 0.06$ and $(\Omega_{\Lambda})_{0} = 0.74 \pm 0.09$. The analysis of deceleration parameter and jerk parameter show that the Universe in derived model is compatible with $\Lambda$CDM model.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

The theories of Evolution and Big Bang have brought a major impact upon the scientific and societal perception upon the origins, abilities and roles of mankind on Earth. It is conclusively evident that Mother Nature and the physical realm is autonomous and all phenomena in the world occur without an imposition against the “free will” of such events and patterns. Nevertheless, this extent of freedom does not imply that life on Earth represents an accident and has no purpose. By careful analysis of ancient religious texts, it can be suggested even otherwise, that it is especially free will that is offered as a gift from outside of the physical dimensions of existence, with the purpose of a continuous edification and improvement of the overall life conditions and of the human perception. It may be that the multi-generational focus on improvement and progress have been misattributed as a long-term evolution of species, that humans came from animal ancestors and that there is a blurred line associating humans with animals. Furthermore, it may be that scientists based their suggestions that no outside Creator would have brought the Earth into existence on physical perspectives, when the extra-dimensional process of Creation implies that all elements of the physical existence undergo a process of Creation from the outside, where time, space and physical matter do not exist, in spite of such elements possibly reflecting unseen elements of the meta-physical world. Finally, there is the following example that deserves attention within the scientific community; just because all living cells - human, animal and plant - contain DNA chromosomes, ribosomes, mitochondria and a plasma membrane, it does not indicate that humans are animals, just as this does not indicate that plants are animals. In Science, there is a golden statement, that correlation does not imply causation. This example is in complete agreement with the verses of the Book of Genesis in the Holy Scriptures regarding the origins of life; namely, that animals could have been created by an Author of all life on Earth so that man would experience companionship. An improved scientific perception of the timeline of life on Earth may be reached via an approach that combines molecular biology with quantum physics, given that the three layers of Science - Biology, Chemistry and Physics - together with their foundational layer of Mathematics, are in fact situated in a relationship of complete harmony.

We think of time as one of four dimensions appearing in the equations of motion of Newtonian and quantum physics, but participating independently of space. In these pages we explore the way the time variable affects how space is perceived. We show first that non-commutation may be interpreted as the difference between electron and photon cycling during radiation processes. For every electron cycle of a quantum oscillator there are two photon cycles. Secondly, the difference between relativistic and non-relativistic quantum mechanics is shown to be related to time evolution. Only relativistic models evolve continuously. The reasoning of Einstein is implicit to an understanding of both physical models. Previously obtained derivations of relativistic quantum mechanics are reaffirmed by following the ideas of Dirac.

A solution is presented that describes a region of space, box or warp bubble, where time gets slowed down by an arbitrary factor, while reducing the components of the energy-impulse tensor by any chosen amount.

The existence of semantic inaccuracy §2 articles by A. Einstein “On the electrodynamics of moving bodies”, illustrating the principle of the relativity of simultaneity. In a sentence “The observers co-moving with the moving rod would thus find that the two clocks do not run synchronously while the observers in the system at rest would declare them synchronous”, the preposition “not” must be moved and placed before the word “synchronous”, at the end of the sentence. The criterion for synchronism of the clocks on the rod is the time it takes for the beam to travel from clock A to clock B and back, and for observers on the rod it will be the same both when the rod is at rest and when the rod is moving. Otherwise, observers on the rod would have had at their disposal an experiment that would allow them to determine whether the rod is moving or at rest, which contradicts the first postulate of the Special Theory of Relativity. The inaccuracy is found unchanged in modern editions in English and Russian, and can become a source of difficulties when teaching the basics of the Special Theory of Relativity based on primary sources, as well as make it difficult to understand the author’s logic when studying independently. Nobel laureate R. Feynman, having expanded and modified A. Einstein's thought experiment, eliminated the inaccuracy described in the article.

When the minimal length approach emerging from noncommutative Heisenberg algebra, generalized uncertainty principle (GUP), and thereby integrating gravitational fields to this fundamental theory of quantum mechanics (QM) is thoughtfully extended to Einstein field equations, the possible deformation of the metric tensor could be suggested. This is a complementary term combining the effects of QM and general relativity (GR) and comprising noncommutative algebra together with maximal spacelike four–acceleration. This deformation compiles with GR as curvature in relativistic eight–dimensional spacetime tangent bundle, generalization of Riemannian spacetime, is the recipe applied to derive the deformed metric tensor. This dictates how the affine connection on Riemannian manifold is straightforwardly deformed. We have discussed the symmetric property of deformed metric tensor and affine connection. Also, we have evaluated the dependence of a parallel transported tangent vector on the spacelike four–acceleration given in units of L, where L = rℏcG3 is a universal constant, c is speed of light, and ℏ is Planck constant, and G is Newton’s gravitational constant.

Disk galaxies have a typical dimension of few tens of thousands of light years. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect is absent in modelling used to calculate rotation curves throughout the entire galaxy and its external gas. The considerable differences between Newtonian action at a distance predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that applying general relativity in a rigorous fashion without mindlessly neglecting retardation, one can explain the radial velocities of galactic matter without modifying gravity or adding unseen matter. Moreover, it was shown that dark matter effects as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. In the original main paper on the subject only one galaxy (M33) was analysed in detail. This was later amended somewhat with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain an excellent fit without postulating dark matter or modifying general relativity.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb-Douglas functions embed the endogenous space factor as new capital to form the space travel firm's production function, which is also transformed into the consumer's utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT presents the equivalence between the spatial geometric tensor and the energy-momentum tensor, which explains the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers' incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and analogy method was applied to infer the space travel pricing by the model of profit maximization, single-minded, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the math models and algorithm. Results show that space travel pricing remains the principle of market equilibrium but needs to be extended to the spacetime tensor of GRT.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. However, the proofs of these theorems traditionally depend upon a collection of assumptions about the continuum spacetime (and, in the physical case, the stress-energy distribution defined over it), including its global structure, its energy conditions, the existence of trapped null surfaces and the various volume/intersection properties of geodesic congruences, that are inherently difficult to translate to the case of discrete spacetime formalisms, such as causal set theory or the Wolfram model. Some, such as the discrete analog of Raychaudhuri's equation for the volumes of geodesic congruences, are subtle to formulate due to intrinsic differences in the behavior of discrete vs. continuous geodesics; for others, such as the definition of a trapped null surface, no appropriate translation is known for the general discrete case due to a lack of a priori coordinate information. It is therefore a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previous work, in which the conformal and covariant Z4 (CCZ4) formulation of the Cauchy problem for the Einstein field equations, with constraint-violation damping, was defined in terms of Wolfram model evolution over discrete (spatial) hypergraphs for the case of vacuum spacetimes, and proceeds to consider a minimal extension to the non-vacuum case by introducing a massive scalar field distribution, defined in either spherical or axial symmetry. Under appropriate assumptions, this scalar field distribution admits a physical interpretation as a collapsing (and, in the axially-symmetric case, uniformly rotating) dust, and we are able to show, through a combination of rigorous mathematical analysis and explicit numerical simulation, that the resulting discrete spacetimes converge asymptotically to either non-rotating Schwarzschild black hole solutions or maximally-rotating (extremal) Kerr black hole solutions, respectively. Although the assumptions used in obtaining these preliminary results are very strong, they nevertheless offer hope that a more general, perhaps ultimately ``Penrose-like'', singularity theorem may be provable in the discrete spacetime case too.

This paper introduces a Unified Field Theory through the generalization of General Relativity, following the methodology outlined by Einstein for incorporating complex metrics in the pursuit of a comprehensive Unified Field Theory.

Galaxies are rather big physical systems having a typical size of tens of kilo parsecs. Thus any change at the center of the galaxy will affect the outskirts only tens of thousand of years afterwards. Retardation seems to be neglected in current calculations of rotational velocities in the far edges of the galaxy and its surrounding gas. The differences between the velocities predicted by Newtonian theory and observational derivations are accommodated by either assuming "dark matter" or by introducing modifications to the laws of gravity in which MOdified Newtonian Dynamics (MOND) is one of the typical examples, celebrating now forty years since its inception. We show that there are overlapping conditions for retardation corrections in the weak approximation to general relativity and the low acceleration conditions for MOND corrections. We will also show that MOND interpolation formula is useful for calculating retardation effects provided an appropriate interpolation function is chosen.

We considered the hypothesis that the sources of dark energy (DE) could be black holes (BHs) or more exotic objects, such as naked singularities or gravastars. We proposed a definition of the presence of DE in the Universe and a criterion for what can be considered the source of this dark energy. It is based on the idea of the accelerated expansion of the Universe, which requires antigravity caused by large negative pressure. A recently proposed hypothesis was examined that mass of BHs increases with time according to the same law as the volume of the part of the Universe containing it and the population of BHs can mimic DE. We demonstrate the reasons why it cannot be accepted, even if all the assumptions on which this hypothesis is based are considered true.

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi–hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric, and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them to reach the center. However in the present case this behavior is affected by the parameter γ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the θ−r subspace. Possible relevance of these results in the explanation of extragalactic jets, is brought out. .

We elucidate the versatility of intriguing symmetry and asymmetry phenomena outside and inside black holes. For description of the test particle (planet and photon) motion it is used the Kerr-Newman metric of the rotating and electrically charged black hole. In particular, it is demonstrated the symmetry and asymmetry of the one-way Einstein-Rosen bridge inside black hole toward and through the plethora of endless and infinite universes.

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper we apply the formalism to derive the metric induced by a `static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized is space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

This is the second in a series of two articles introducing the Gravitas computational general relativity framework, in which we now focus upon the design and capabilities of Gravitas's numerical subsystem, including its ability to perform general 3+1 decompositions of spacetime via the ADM formalism, its support for the definition and construction of arbitrary Cauchy surfaces as initial data, its support for the definition and enforcement of arbitrary gauge and coordinate conditions, its various algorithms for ensuring the satisfaction of the ADM Hamiltonian and momentum constraints, and its unique (totally-unstructured) adaptive refinement algorithms based on hypergraph rewriting via Wolfram model evolution. Particular attention will be paid to the seamless integration between Gravitas's symbolic and numerical subsystems, its ability to configure, run, analyze and visualize complex numerical relativity simulations and their outputs within a single notebook environment, and its capabilities for handling generic curvilinear coordinate systems and spacetimes with general (and often highly non-trivial) topologies using its specialized and highly efficient hypergraph-based numerical algorithms. We also provide illustrations of Gravitas's functionality for the visualization of hypergraph geometries and spacetime embedding diagrams in two and three dimensions, the ability for Gravitas's symbolic and numerical subsystems to be used in concert for the extraction of gravitational wave signals and other crucial simulation data, and Gravitas's in-built library of standard initial data, matter distributions and gauge conditions. We conclude by demonstrating how the numerical subsystem can be used to set up, run, visualize and analyze a standard yet nevertheless reasonably challenging numerical relativity test case: a binary black hole collision and merger within a vacuum spacetime (including the extraction of its outgoing gravitational wave profile).

Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation gives a relationship between the mass ratio and the final velocity in multiples of the exhaust speed, and dictates a high mass ration for current exhaust speeds. A relativistic motor exchanging momentum and energy with the electromagnetic field may mitigate such considerations, enabling efficient interplanetary travel. In this paper we will discuss the advantages and challenges of this novel mover for space transportation.

When generalized noncommutative Heisenberg algebra accommodating impacts of finite gravitational fields as specified by loop quantum gravity, doubly–special relativity, and string theory, for instance, is thoughtfully applied to the eight-dimensional manifold (M8), the generalization of the Riemannian manifold becomes imminent. By constructing the deformed affine connections on a four-dimensional Riemannian manifold, we have determined the minimal length deformation of Riemann curvature tensor and its contractions, the Ricci curvature tensor, and Ricci scalar. Consequently, we have been able to construct the deformed Einstein tensor. As in Einstein’s classical theory of general relativity, we have proved that the covariant derivative of the deformed Einstein tensor vanishes, as well. We conclude that the minimal length correction suggests a correction to the spacetime curvature which is manifest in the additional curvature terms of the corrected Riemann tensor and its contractions. Accordingly, the spacetime curvature endows additional curvature and geometrical structure.

A Teoria das diferenças entre elementos explica as razões das diferenças nos conceitos físicos entre diferentes elementos, como a Física Quântica e a Teoria da Relatividade Geral, sendo explicada através de observações. Assim, é possível concluir a partir das observações que as diferenças são motivadas pelas reações entre os elementos, pela composição dos elementos, e pela influência dos espaços que promovem perdas e ganhos de características; portanto, não há semelhança geral entre a física quântica e a teoria geral da relatividade. O estudo tem como objetivo compreender os elementos e seus conceitos físicos que compõem o Universo.

The study of emission, propagation, and reflection of balls in Newtonian mechanics, employing the laws of conservation of momentum and energy when the mass of balls converges to zero, concludes that the kinematics of light is like that of massless balls. The kinematics of light explains why light speed is the constant in each inertial frame in which the light source and reflective mirror are at rest, why the laws of physics have the same form in each inertial frame, and why any experiment in an inertial frame cannot prove the motion of that the other inertial frame. The theory of special relativity misapplies symmetry observed in phenomena to two inertial frames; therefore, it duplicates a physics phenomenon from one inertial frame, considered stationary, into another. Moreover, Lorentz’s transformation offers light speed at the constant in the moving and opposite direction of the inertial frame but is variable in any other direction. Therefore, the theory of special relativity rejects itself with these unacceptable conclusions.

Abstract: Experiments conducted to date to verify the relativistic gravitational time dilation have limited scientific significance because the basic postulate of Einstein’s relativistic GR that the same time (t0) is measured in all non-inertial frames of reference, because all non-inertial frames of reference must be equal, has not yet been verified by time measurements. According to Einstein's relativistic GR, a correlation between time and different gravitational potentials must be the result of a relative relation between non-inertial frames of reference and must not the result of any other physical influence. An experiment that can differentiate between a causal correlation (relative relation) and an apparent correlation (relativistic relation) between time and gravitational potentials is still outstanding. The expressions "relative" and "relativistic" are often used as synonyms. However, Einstein's GR is a relativistic theory. In the case of general relativity, relativistic means that time depends only on the relative relation between non-inertial frames of reference and not on other physical factors. The author proposes an easy-to-realize experiment that is able to distinguish between a causal correlation (relative relation) and an apparent correlation (relativistic relation) between time and gravitational potentials, which can confirm or falsify Einstein's relativistic GR. .

We demonstrate that multiple well-known metrics, such as the Schwarzschild metric and the extremal solution of the Reissner-Nordstr ̈om metric, can be expressed in what we will call thermodynamic form. These formulations appear to be valid for all Rs = ct growing black holes and, therefore, also within the framework of Rh = ct growing black hole cosmology. However, the metrics can also be applied to non-black hole gravitational objects as long as one calculates the CMB and Hawking temperature of the hypothetical black hole from the gravitational mass.

This article begins with exploring fundamental limits in the universe. It examines key principles, such as the uniformity of physical laws and Energy conservation, that lead to maximum speed, locality, and maximum density. These universal limits govern physical phenomena, leading to very interesting results.I demonstrate that quarks and leptons comprise smaller entities named "Quantum Black Holes." These Quantum black holes are relativistically rotating miniature charged black holes consisting of a single core at the highest possible density. Quantum black holes are the only structures small enough in space-time capable of keeping all charges quantized (including gravitational charges.)By the end of the article, I prove that Quantum black holes explain the deficiencies of SM. They facilitate explanations of quantized gravity, the nature of Luminous and dark Matter, establishing the Mass, size, and (quantized) charges quantities of elementary particles, the nature of neutrino oscillations, and more. Elementary particles release their Energy outward, altering the curvature of nearby space-time and providing new insights into the nature of space-time curvature change. With this understanding, we can characterize movements and processes in local space-time using five sets of equations simultaneously: four representing the four charge types and one representing Dark Matter.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

This paper is a brief review of our own work on the Planck quantized version of general relativity theory. It demonstrates several other straightforward methods to simply rewrite the same equations that we have already presented.

This article presents a novel approach to understanding the influence of electric Energy on space-time curvature. EFE actual calculations refer solely to gravitational charges. In this article, I expand them to include the electric charge with calculations carried specifically for electric charges, with exciting results. The article leverages the universal consistency of physical laws, applying the known effects of gravitational charges on space-time curvature to electric charges. The research focuses on calculating the specific impact of electric charges on space-time curvature, rooted in the principle that space-time curvature is omnipresent. The findings reveal that space-time curvature's alteration due to an electric charge is influenced by various factors, including the charge's location, magnitude, mass, density, associated electric field, and its motion through space-time. Notably, the conversion factor for electric charges differs from the conversion factor for gravitational charges. These insights significantly enhance our understanding of electromagnetism and general relativity, paving the way for a more profound comprehension of electric charges.

Recent efforts to conceptually design a technologically meaningful electromagnetic retarded engine indicated that this can only be done using the immense charge and current densities which exist in the atomic scale. However, this scale cannot be described by Newtonian physics, and only a quantum description will suffice to describe the dynamics of an electron on this scale properly. Here we study the retarded field quantum engine and highlight the differences between the quantum and the classical retarded engines.

The paper suggests that the physical priciple of special relativity's space-time transformation effect is wrong, Uniform linear motion without acceleration does not exist objectively, nor does its same reference frames. Therefore, it is inferred that the space-time transformation effect of special relativity is caused by the acceleration of moving objects, special relativity is only a part of general relativity, not a theoretical system that exists independently from general relativity. The corresponding mathematical demonstration and calculation verification are carried out, and the result proves that the inference of the paper is correct. At the same time, it further explains that the concept of absolute airspace is correct. Special relativity has serious errors in the concept of space, the principle of relativity and the physical principle of space-time transformation effect. Therefore, it is necessary to make a series of revisions to the theory of relativity and to reinterpret some related physical problems.

We proposed an equation of motion as a constraint condition on the gauge degree of freedom in general relativity theory based on a co-moving framework. This constraint equation transformed the gauge degree freedom of general relativity theory into an natural equation of motion, and provide an explicit theoretical understanding on the Mach's principle and rotating bucket experiment. The galaxy rotation curves is derived directly from general relativity theory under this constraints equation. This work may inspires different understanding on dark matter, dark energy, and the quantization of gravity.