In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

By combining general relativity and CPT symmetry, the theory of CPT gravity predicts gravitational repulsion between matter and CPT-transformed matter, i.e. antimatter inhabiting an inverted space-time. Such repulsive gravity turned out to be an excellent candidate for explaining the accelerated expansion of the Universe, without the need for dark energy. The recent results of the ALPHA-g experiment, which show gravitational attraction between antihydrogen atoms and the Earth, seem to undermine this success in the cosmological field. Analyzing the above theory, we find two solutions that can be consistent with the experimental results, while preserving the large-scale gravitational repulsion. The first highlights how repulsive gravity can be the result of the interaction with an inverted space-time, but occupied by matter and not antimatter, and therefore the antimatter present in our space-time has no reason to exhibit gravitational repulsion. The second retains the original CPT transformation, resulting in repulsive gravity between matter and antimatter, but with the caveat that antimatter immersed in our space-time cannot exhibit the PT transformation which is the cause of the repulsion. Finally, it is shown that, in a Newtonian approximation of the geodesic equation, time reversal is not a necessary operation for repulsive gravity, therefore opening the possibility of an expanding cosmos with a single time direction.

Various techniques to tackle the black hole information paradox have been proposed. A new way out to tackle the paradox is via the use of pseudo-density operator. This approach has successfully dealt the problem with a two-qubit entangle system for a single black hole. In this paper, we present the interaction with a binary black hole system by using an arrangement of the three-qubit system of Greenberger–Horne–Zeilinger (GHZ) state. We show that our results are in excellent agreement with the theoretical value. We have also studied the interaction between the two black holes by considering the correlation between the qubits in the binary black hole system. The results depict a complete agreement with the proposed model. In addition to the verification, we also propose how modern detection of gravitational waves can be used on our optical setup as an input source, thus bridging the gap with the gravitational wave’s observational resources in terms of studying black hole properties with respect to quantum information and entanglement.

For a hierarchy of large scale structures, like galaxies, galaxy clusters, super-clusters, etc. the requirement that their gravitational (binding) self-energy density must at least equal or exceed the background repulsive dark energy density implies a universal mass-radius relation given by M/R² ~ 1g/cm². Here we point out that this mass-radius relation also holds for important individual biological structures, and even various organisms as a whole such as humans, trees, and to behemoths like whales, even though the physics is different. Here we try to understand this universality from two different physical considerations. We also point out the coincidence that the densities of most biological entities are close to that of water, and that the average density of main-sequence stars and giant planets are close to this density. We give a physical basis for the same.

Swimming pools are examples of water-intensive facilities, where solutions for reducing economic and environmental costs are increasingly frequently searched. One of the solutions is the recovery of water from wastewater, including from washings obtained through the process of rinsing filter bed. The study objective was the qualitative and quantitative assessment of post-coagulation sludges, the main pollutant found in the washings. During the analyses, assessment of the sedimentation capabilities of the sludges was performed (gravitationally), particle size distribution was assessed (particle size distribution analyzer) and assessment of phytotoxicity with the use of plant indicators in short-term tests was performed (Lemna minor, Lepidium sativum, Sinapis alba, Raphanus sativus). The samples were collected from two independent circulations, which differed in terms of capacity and type of coagulant used. The tested post-coagulation sludges were characterized by high content of total suspended solids: in samples from Circulation 1 from 251 to 128 mg/l, in Circulation 2 from 489 to 228 mg/l. However, the sedimentation processes enabled significant separation of sludges. The hydrolyzed coagulant contributed to the improvement of sedimentation capabilities of sludges. Despite the fact that in many samples low sludge concentrations favored stimulation of plant growth, the post-coagulation sludges can constitute a hazard to plant growth, particularly in the long-term perspective.

This article analyzes in detail the influence of Jupiter on the measurement of the gravitational constant. Including a specific estimate of the change in the gravitational constant caused by the change of the earth's orbital position every half month. The influence of Jupiter's perihelion and aphelion on the gravitational constant is also estimated. On this basis, this article analyzes the data with specific time records such as BIPM-01, BIPM-14, JILA-10, UCI-14, HUST-09. The analysis results show that after considering the influence of Jupiter, the experimental results have been significantly improved.

Three body systems in which one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study this phenomenon qualitatively, we try to expand this problem's scope to unequal mass systems and generalize them by considering various configurations of fixed initial points with precisely calculated initial velocities, some zero velocity models and some optimized models. We will see the use of terminology similar to the previous studies done in this domain but incorporate different analytical and evaluation methods.

Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analysing the situation without neglecting Mercury’s mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too strong for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too strong. ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted.

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.

After proposing the Principle of Minimum Gravitational Potential, in a pursuit to find the explanation behind the correction to Newton's gravitational potential that accounts for Mercury's orbit, by finding all the higher-order corrections it is shown that the consequences of the existence of speed of light for gravity are not yet fully explored.

The experiment proposed by Bose et al aims to show the non classicality of gravity through entanglement. This paper seeks to establish optimal conditions under which the entanglement would be maximized. The assumptions made by Bose et al to come to the conclusion of quantized gravity would also be discussed along with alternate conclusions that could arise from the experiment.

G4v is a four-vector theory of gravitation proposed by Mead (2015, 2023a,b) which reinterprets several major results commonly celebrated for the tensor-based approach of General Relativity (GR). Here, we show that G4v obeys the correspondence principle, an important test of any relativistic theory. We derive the non-relativistic Lagrangian and Energy expressions at the limit of low speeds and potentials, complete with the correct terms for potential energy (something traditional Special Relativity is incapable of achieving). G4v could represent a new interpretation of the gravitational field with essentially the same mathematics as electromagnetism (Mead 2023a). It is also possible to interpret G4v as a very interesting (and useful) approximation of the Einstein field equations (Mead 2023b).

Using the principle of equivalence, it has recently been shown that the electrostatic field lines of a charge, stationary in the gravitational field, bend exactly like the trajectories of photons emitted isotropically from a source at the charge location and that the fraction of electric flux crossing a surface `below' or `above' the charge is exactly similar to the fraction of photon trajectories intersecting these surfaces, with more flux in the downward direction than upward. As one goes much deeper in the gravitational field, all electric field lines increasingly point in the vertically downward direction as is also the case for a stream of photons. Since photon trajectories as well as electric field lines, at any location in the gravitational field, are affected by the local space-time curvature an inference can be drawn that this parallel between the photon trajectories and the electric field lines is a general result. We could then apply these results in the external gravitational field of a black hole, where the trajectories of photons in the gravitational field are already well-known and the behaviour of electric field lines of a stationary charge could be inferred therefrom. Accordingly, we show that the electric field through an external spherical surface surrounding the black hole steadily reduces as the charge location approaches the event horizon (Schwarzschild radius), and like photons from a source inside the Schwarzschild radius cannot escape outside, the electric field lines of a charge within the black hole too remain trapped inside the event horizon. From this one arrives at a conclusion that, contrary to the conventional wisdom, the electric charge contained inside a static black hole cannot be detected or inferred by an external observer. A black hole, said to have no hair with the only external identifying characteristics being mass, electric charge, and angular momentum, is therefore all the more `hairless', as even its charge cannot be ascertained. The derivation of the Reissner-Nordström metric, supposedly describing the gravitational field of a static charged black hole, presumes an external stress-energy tensor of the electrostatic field, as per Gauss law, even for the charges contained within the black hole. However, the absence of electric flux external to a static charged black hole implies that such a charged black hole is not described correctly by the Reissner-Nordström metric and the consequential peculiarities of the space-time geometry, leading in specific cases to the idea of a naked intrinsic singularity and a need for the ``cosmic censorship'' hypothesis, also do not arise here.

This research explores the intricate relationship between gravitational and cosmic redshift phenomena, unveiling a profound understanding of how light behaves as it traverses the cosmos. The study begins with an examination of gravitational redshift, a well-established concept occurring when photons move away from massive gravitational sources, such as stars within galaxies. Gravitational redshift, expressed as λ/λ₀, manifests within the gravitational influence and extends to the boundary of the observed "zero-gravity sphere" enveloping galaxies. Within this remarkable zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. As a result, gravitational redshift dominates, and cosmic redshift is notably absent within the sphere. Photons within this sphere maintain their constant speed 'c' and undergo gravitational redshift exclusively. However, as photons exit the zero-gravity sphere at a distance 'r' equivalent to the source star's radius, they encounter the onset of cosmic redshift, quantified as {(λ_obs - λ_emit)/ λ_emit}. Cosmic redshift blends with gravitational redshift, forming the effective redshift of the photon. Critically, the effective cosmic redshift surpasses gravitational redshift, illuminating a profound revelation: photons traverse a greater "light-traveled distance" than their proper distance from the source. In essence, cosmic redshift signifies that photons move across their intended distances at their intrinsic speed c, while the expanding universe introduces a relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, shedding light on their remarkable implications for our comprehension of the expanding universe.

In this paper, we consider particles together with the surrounding space as an indivisible system, and then investigate the maximum symmetry of the system at the quantum level. We introduce a new quantity to describe the evolution of this system before and after measurement. The effective mass of gravity is estimated. We also show that a free quantum particle as the source of energy and momentum do not produce gravity.

Community centers play a crucial role in urban environments, providing physical and educational services to their surrounding communities, particularly for students. Among the many benefits for students are enhanced academic outcomes, improvement of behavioral problems, and increased school attendance. Such centers are also particularly vital for low-income and racial minority students as they are pivotal in giving them outside-of-school learning opportunities. However, determinants influencing attendance at community centers remain largely unexplored. Using census data, Boston Centers for Youth and Families (BCYF) attendance data, and specific center attributes, we develop human mobility gravitational models to predict attendance across the BCYF network. Using those models, we investigate the potential effects on general and student attendance by changing center attributes, such as facilities and operating hours. We also research the impact of changing the walking accessibility to those centers on their respective attendance patterns. After the analysis, we find that the most cost-effective policy to increase BCYF attendance is changing each center’s educational and recreational offerings far beyond any accessibility interventions. Our results provide insights into potential policy changes that could optimize the attendance and reach of BCYF Community Centers to underserved populations.

The gravitational constant is an unchanging quantity included in the law of universal gravitation. The value of this constant is known much less accurately than other fundamental physical constants, which is due to the experimental difficulties of measuring it. Here we report a simple method for the theoretical calculation of the gravitational constant using the elementary charge, speed of light, Z boson mass, and relativistic mechanics.

We introduce quantum spatio-temporal dynamics (QSD) as modeled by the Nexus Paradigm (NP) of quantum gravity to resolve the problem of energy- momentum localization in a gravitational field. Currently, the gravitational field as described using the language of geometry modeled under General Relativity (GR) fails to provide a generally accepted definition of energy-momentum. Attempts at resolving this problem using geometric methods have resulted in various energy-momentum complexes whose physical meaning remain dubious since the resulting complexes are non-tensorial under a general coordinate transformation. In QSD, the tangential manifold is the affine connection field in which energy-momentum localization is readily defined. We also discover that the positive mass condition is a natural consequence of quantization and that dark energy is a Higgs like field with negative energy density everywhere. Finally, energy-momentum localization in quantum gravity shows that a free falling object will experience large vacuum fluctuations (uncertainties in location) in strong gravity than in weak gravity and that the amplitudes of these oscillations defines the energy of the free falling object.

We investigate the evolution of gravitational waves through discontinuous evolution (transition) of the Hubble expansion rate H(z) at a sudden cosmological singularity which may be due to a transition of the value of the gravitational constant. We find the evolution of the scale factor and the gravitational wave waveform through the singularity by imposing the proper boundary conditions. We also use existing cosmological data and mock data of future gravitational wave experiments (the ET) to impose current and anticipated constraints on the magnitude of such a transition. We show that mock data of the Einstein Telescope can reduce the uncertainties by up to a factor of 3 depending on the cosmological parameter considered.

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.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

We show that the entropy or information flow of a gravitational system constrains the dependence of gravitational force on radial distance r which for very large r is equivalent to gravity in two dimensions. This explains the "origin" of dark matter and provides a natural solution to the problem of flat rotation curves of galaxies at very large distances and a larger deflection angle for a gravitational lens.

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.

This Thesis is concerned with one of the most promising probes to constrain the "Dark Universe", and, particularly, the dark matter distribution. Based on MICE cosmological simulation, and the all-sky convergence maps generated by Fosalba et al. [58], we perform a mass calibration of the dark matter halos there contained up to z=1. In order to do that, we analyse the average halo density proÖles of all the halos with masses ranging from 5E13 to 3.75E14 M/h , divided into four mass bins and three redshift bins. Through this analysis we address two main issues: the relatively low mass resolution of the simulation (mp=2.34E11M/h) and the relatively high softening length (lsoft=50Kpc/h). We do that by using a two-step procedure. First, we simulate analytical pure NFW density proÖles (with di§erent mass resolutions) using two input values: the virial radii of MICE halos and the expected concentrations, according to the Öxed mass-concentration relation from Oguri and Hamana [130]. Second, we model the e§ect of the softening length with a Gaussian Ölter, smoothing the halo core. The results show that MICE halos are, in average, NFW halos. Best-fit NFW radii are in very good agreement with the average radii of our samples, overestimating the data by ~1%, but best-fit NFW concentrations are in average 50% lower than the expected values. It is possible to account for part of this deviation by distinguishing between relaxed and unrelaxed halos, finding that, depending on the degree of relaxedness, the improvement can be as high as 30%. We also find that the analytical NFW halos simulated with MICE mass resolution have an overall concentration 40% lower than the input concentration, in the case of 3D proÖles, and 25% lower in that of the projected profiles. The Gaussian-smoothed NFW profile is a good approximation for our projected halos. Additionally, we analyse the morphology of the halos, characterizing their triaxiality at R200 and calculating their orientation with respect to the line-of-sight (LOS). MICE halos tend to adopt a more prolate morphology, as might be expected from a CDM simulation (Shaw et al. [159]), and the percentage of prolate halos grows as their mass grows. The mass resolution is, nonetheless, not good enough to draw conclusive inferences from the shape analysis, but it allows us to discern a trend and estimate the e§ect of halo shape and orientation on the weak lensing masses. Finally, we use the all-sky convergence maps to study the scatter in mass measurements of MICE halos. We determine the intrinsic scatter in the recovered masses by assuming the smoothed NFW profile as the 'true' profile, and creating two new convergence maps from different mass cuts. We estimate also the scatter due to the correlated structure by studying the angles between the major axes of the halos and the LOS, and also that due to projection e§ects (i.e. all the dark matter between observer and source). We Önd an irreducible scatter (intrinsic) of 10-14%, a scatter around a 30% of the intrinsic one due to correlated structure, and a scatter around 40-70% of the intrinsic one due to projection e§ects. The size of our halo sample allows us to improve the characterization of the cosmic noise, of great importance for present and future surveys.

We propose that, at equilibrium, statistically equal temperatures as mechanical torques are exerted on each kind of gas phase molecules as rates of translational action [@t=ʃmvds/dt=ʃmr2ωdϕ/dt=mv2, J]. These torques result from the impulsive density of resonant quantum fields with molecules, configuring the trajectories of gas molecules while balancing molecular pressure (p=NkT) against the density of field energy (J/m3). Gibbs energy fields contain no resonant quanta at zero Kelvin, with this measure of chemical potential diminishing in magnitude as translational action of the vapor molecules and quantum field energy increases with temperature. In illustration, we show how impulsive torques from quantum fields drive the reversible thermodynamics of Carnot’s heat-work engine cycle, sustain the decreasing atmospheric temperature gradient of increasing molecular entropy with altitude, support the translational action and field energy of vortical wind flow in anticyclones, frictionally warming the Earth’s surface while recycling greenhouse infrared absorption of surface radiation, generating electrical power from air flow in wind farms and destructive power in tropical cyclones. These cases all distinguish symmetrically between a causal field of impulsive quanta (Σhν) that energizes the action of matter and the resultant vis viva of molecular mechanics (mv2). The quanta of these different fields display mean wavelengths from 10-4 m to 1012 m, with mechanical advantages many orders of magnitude greater than the corresponding translational actions, though with mean quantum frequencies (v) similar to those of radial Brownian movement for independent particles (ω). These energy fields are also thermodynamically reversible reservoirs for heat, optimizing work processes on Earth and delaying the achievement of maximum entropy production from short wave solar radiation in conversion to outgoing long wave radiation to space.

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.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes with a mass range of approximately 104∼107M⊙. EMRIs are estimated to produce long lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the high-dimensional and large-volume parameter space, make the fully coherent search challenging. In our previous work, we proposed a 10-dimensional search using Particle Swarm Optimization (PSO) with local maximization over the three initial angles. In this study, we extend the search to an 8-dimensional PSO with local maximization over both the three initial angles and the angles of spin direction of the MBH where the latter contribute a time independent amplitude to the waveforms. Additionally we propose a 7-dimensional PSO search by using a fiducial value for the initial orbital frequency and shifting the corresponding 8-dimensional Time Delay Interferometry responses until a certain lag returns the corresponding 8-dimensional log-likelihood ratio maximum. The reduced dimensionality likelihoods enable us to successfully search for EMRI signals with duration of 0.5 years and signal-to-noise ratio of 50 within a wider search range than our previous study. We discuss further developments, such as using a hierarchical search to narrow down the search ranges of certain parameters, and applying Graphics Processing Units to speed up the code. These advances aim to improve the efficiency and accuracy of the EMRI search algorithm.

In this research, we investigate the bending of photon light and/or time-like geodesics within the context of four-dimensional space-time geometry, specifically in the presence of topological defects. These topological defects manifest as cosmic string space-time configurations, encompassing screw dislocation, spiral dislocation, and spacelike dislocation. Our primary objective is to determine the extent of deflection experienced by light-like and time-like geodesics and analyze how this deflection is affected by the cosmic string parameter, screw dislocation parameter, and spacelike dislocation parameter. To accomplish this, we employ a derivation technique that centers on the observation that photon rays (light-like geodesics) and/or time-like geodesics follow paths parallel to the z-axis while maintaining a constant radius along the cylinder.

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.

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

The gravitational constant is equivalent to natural units in its six unit dimensions. Evaluating the classical formulas in each unit dimension shows how inputs of mass and radius are transformed into the correct unit dimensions and magnitude of gravitational potential. Mass and radial distance are equivalent proportions of the Planck scale as the potentials they produce. Gravitational potentials of velocity, acceleration, energy, and force are proportional to a radial density limit of one Planck mass per Planck length of radial distance.

In physics, symmetry is mostly about the symmetry between elementary particles, between matter and antimatter. In the universe, we have two fundamental types of energy: energy of matter and energy of space. These two energies have a symmetry that is not geometry type, not electric charge type, it is energy type. Every physical object with mass m symmetrically diminishes the energy density of space in its center exactly for the amount of its mass. This symmetry of matter and space energies is the physical source of gravity that is also valid in the centre of black holes.

In 1911, A. Einstein suggested that gravity affects at the electromagnetic radiation originating from the distant sources, namely, it shifts the spectral lines in the red side of the spectrum and derived the gravitational redshift formula. A modern science claims that Einstein’s formula is mathematically immaculate. We show that this is not true: in fact, this formula is approximate. Using the law of conservation of mechanical energy, we derived two exact formulas оf the gravitational redshift.

In our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, e_n=2.95e and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. The aim of this paper is associated with understanding the mystery of quantum of magnetic flux, Planck’s quantum radiation constant and Reduced Planck’s constant. Proceeding further, quark charges, strong coupling constant, nuclear stability, nuclear binding energy, medium and heavy atomic X-ray levels and celestial magnetic moments can be understood in a unified approach. It may also be noted that, by considering integral nature of elementary particle masses, it seems possible to understand the discreteness of angular momentum. Considering our proposed e_n=2.95e=3e as a characteristic nuclear charge, it seems possible to understand the integral nature of quarks electromagnetic charge. With this idea, neutron, proton and pions decay can be understood very easily. In all the cases, up quark of charge (±2e) seems to play a crucial role with the internal transformation of down quark of charge (±e) and external observable elementary basic elementary particles. It needs further study at fundamental level.

The saturation properties of symmetric and asymmetric nuclear matter have been computed using the finite range simple effective interaction having Yukawa form-factor. The results of higher order derivatives of the energy per particle and the symmetry energy computed at saturation, namely, Q0, Ksym, Kτ, Qsym, are compared with the corresponding range of values extracted from studies involving theory, experiment and astrophysical observations. The ability of the equations of state computed with this simple effective interaction in predicting the threshold mass for prompt collapse in binary neutron star merger and gravitational redshift have been examined in terms of the compactness of the neutron star and the incompressibility at the central density of the maximum mass star. The correlations existing between neutron star properties with the nuclear matter saturation properties have been analyzed and compared with the predictions of other model calculations.

Swarm intelligence (SI) methods are nature-inspired metaheuristics for global optimization that exploit a coordinated stochastic search strategy by a group of agents. Particle Swarm Optimization (PSO) is an established SI method that has been applied successfully to the optimization of rugged high-dimensional likelihood functions, a problem that presents the main bottleneck across a variety of gravitational wave (GW) data analysis challenges. We present results from a first application of PSO to one of the most difficult of these challenges, namely, the search for Extreme Mass Ratio Inspiral (EMRI) in data from future spaceborne GW detectors such as LISA, Taiji, or Tianqin. We use the standard Generalized Likelihood Ratio Test formalism, with minimal use of restrictive approximations, to search 6 months of simulated LISA data and quantify the search depth, in signal-to-noise ratio (SNR), and breadth, in the ranges of the EMRI parameters, that PSO can handle. Our results demonstrate that a PSO-based EMRI search is successful over a search region that is in the ballpark of the one that current hierarchical schemes can identify. Directions for future improvements, including computational bottlenecks to be overcome, are identified.

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature $T$ in thermal equilibrium with a black-body. Each particle of this exotic gas mimics a kind of particle of dark energy. So, each dark particle occupies a very small area of space so-called Planck area $L_p^{2}$, which represents the minimum area of the whole space-time given by the spherical surface with area $4\pi R_H^2$, where $R_H$ is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of $\sim 10^{-17}$Hz due to the slight stretching of the fabric of space-time.

I argue that the main feature of elliptical space – the topological identification of its antipodal points – might be behind some observational facts on both cosmological and microscopic scales. I use calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” for distance measure in cosmology. These are compared with the observational data collected in a catalogue called “Pantheon+”. On the microscopic scale I show that a physical elliptical space, in which the mathematical connectedness between antipodal points is replaced with physical connections via the Einstein-Rosen bridges (also called “wormholes”), gives rise to sub-particle structures similar to J.A. Wheeler’s geons. The interactions between these structures leading to their equilibrium configurations can explain the experimentally observed pattern of properties of elementary particles forming the standard model of particle physics. The answer to the question why we have this particular set of fundamental particles might lie in the fundamental properties of elliptical space.

It is shown that de Sitter accelerated expansion of the Universe (dark energy effect) is an exact solution to the set of self-consistent stochastic nonlinear gravitational waves in the FLRW metric coming to the Universe from “nowhere”.

A semi–numerical approach proposed many years ago for describing gravitational collapse in the post–quasi–static approximation , , , , is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi–homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post–quasi–static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

It has been theorized that black holes are surrounded by firewalls, although there is not universal agreement concerning this. We first review basic concepts pertaining to Schwarzschild black holes and Hawking radiation. Then we discuss the anticipation of Hawking radiation—albeit from non-black holes—initially by R. C. Tolman and shortly thereafter with P. Ehrenfest. We compare evaporation into a vacuum at absolute zero (0 K) of black holes with that of non-black holes, and show that not only black holes but also non-black holes evaporate within a finite time. The times required for evaporation of black holes and non-black holes are compared. Next, we show that (i) if firewalls exist, they can originate via Hawking radiation at the minimum possible ruler distance (the Planck length) beyond the Schwarzschild horizon, where it has not suffered any gravitational redshift, or, alternatively, suffered maximal gravitational blueshift and (ii) the firewall temperature is on the order of the Planck temperature, independently of the mass and hence also of the Schwarzschild radius of a Schwarzschild black hole. We then explain the exponential nature of the gravitational frequency shift as a function of the gravitational potential. Next, we consider the firewall-mass problem, and provide an at least prima facie tentative resolution thereto based on: (i) the mass of a firewall being canceled by the negative gravitational mass = (negative gravitational energy)/c² accompanying its formation, (ii) the unchanged observations of a distant observer upon formation of a firewall, and (iii) Birkhoff's Theorem (actually first discovered by Jørg Tofte Jebsen). We then consider one aspect of thermodynamics in gravitational fields, showing that equilibrium relativistic gravitational temperature gradients cannot be exploited to violate the Second Law of Thermodynamics.

Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main sources. Numerical simulation is an effective method to investigate the impact of perturbation on spacecraft orbits. This study shows that, in the context of the Taiji project, Earth’s gravity is an essential factor in the change in heliocentric formation configuration, contributing to the relative acceleration between spacecrafts in the order of O(10−6)m·s−2. Considering 00:00:00 on October 27, 2032 as the initial orbiting moment, under the influence of Earth’s gravitational perturbation, the maximum relative change in armlengths and variation rates of armlengths for Taiji is 1.6×105km, 32m·s−1 respectively, compared with the unperturbed Keplerian orbit. Additionally, by considering the gravitational perturbations of Venus and Jupiter, the armlength and relative velocity for Taiji are reduced by 16.01% and 17.45%, respectively, compared with when only considering that of Earth. The maximum amplitude of the formation motion indicator changes with the orbit entry time. Results show that the relative velocity increase between the spacecrafts is minimal when the initial orbital moment occurs in July. Moreover, the numerical simulation results are inconsistent when using different ephemerises. The differences between ephemeris DE440 and DE430 are smaller than those between DE440 and DE421.

Aiming at the development of the application of massive and heterogeneous LEO constellations, the influence of typical perturbation forces on the orbit prediction of LEO satellites at different altitudes is analyzed. Firstly, the main perturbation force model of LEO satellites is introduced. Then experiments for analyzing the influence of orbit prediction on LEO satellites at different altitudes are designed. Finally, the influence of typical perturbation forces on the orbit prediction under different prediction durations by numerical analysis is assessed systematically, and the orbit prediction of LEO satellites with different non-spherical gravitational field orders, ocean tide orders and atmospheric density models were compared and calculated. The research results show that different orders of non-spherical gravitational fields should be considered when the altitude of satellites is different, the reasonable gravitational field orders for LEO satellites at 500km, 1000km, 1500km and 2000km under 1-hour forecast time are 140x140, 80x80, 60x60 and 40x40 orders, the reasonable orders of ocean tide perturbation for 1500km and 2000km satellites are 20x20 orders. Under the 24-hour forecast time, atmospheric resistance has a great influence on the precision of LEO satellites at orbit altitude below 1,000km. The forecast deviation of the LEO satellites orbit at 500km reaches 8751.576m. The difference of orbit precision between different atmospheric density models is in the meter level. The orbit deviation by the Standard Atmosphere 1976 and NRLMSISE 2000 atmospheric models respectively reaches 25.494m. Relevant conclusions provide support for the optimization and selection of dynamical models in high precision orbit determination and fast orbit prediction of LEO satellites.

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. .

The concept of a black hole is examined through a historical lens, emphasizing the distinctions between its mathematical definition and the observed phenomena in the cosmos. An essential point of contention is highlighted, the challenge of reconciling the ultimate state of gravitational collapse, conceptualized as a black hole with its associated future event horizon, with the vast age of the universe as measured in cosmic time. The work delves into the evolution of black hole theories, tracing their development from the early mathematical solutions, such as the Schwarzschild solution, to the contemporary understanding shaped by contributions from Hawking and Penrose. The complex interplay between mathematical descriptions and observational realities is explored, shedding light on the difficulties inherent in merging theoretical concepts with astrophysical observations. A particular focus is placed on the discrepancy between the theoretical formation of a black hole and the seemingly infinite cosmic time required for the collapse process according to the seminal work of Oppenheimer and Snyder. This apparent incongruity raises questions about the nature of objects labeled as black holes in astrophysics and prompts a critical examination of how observational data align with theoretical predictions. In essence, this exploration underscores the need for a nuanced and critical analysis of the concept of black holes, considering the intricate interplay between theoretical constructs and empirical observations within the framework of General Relativity.

The gravitational potential characterizes the gravitational field of ordinary bodies and has dimension equal to the square of the velocity. In 2021, a new expression for the law of universal gravitation was obtained, which is completely analogous to Coulomb’s law. Using this result, the presented paper introduces a new formula for the gravitational potential, which has dimension of velocity. This formula establishes a clear boundary for the mass of objects that are transitive from giant planets to stars of the smallest masses (brown dwarfs).

High-precision inertial sensors or accelerometers can provide us references of free-falling motions in gravitational field in space, and serve as the key payloads for gravity recovery missions. In this work, a systematic method of electrostatic inertial sensor calibrations for gravity recovery satellites is introduced, which is applied to and verified with the Taiji-1 mission. Taiji-1 is the first technology demonstration satellite of the ``Taiji Program in Space'', which, in its final extended phase in 2022, could be viewed as a gravity recovery satellite operating in the high-low satellite-to-satellite tracking mode. Based on the calibration principles, swing maneuvers with time span about 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. The inertial sensor's operating parameters including the scale factors, the center of mass offset vector and the intrinsic biased acceleration are precisely re-calibrated and are updated to the Taiji-1 science team. Data from one of the sensitive axis is re-processed with the updated operating parameters, and the performance is found to be slightly improved compared with former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the planned Next Generation Gravity Missions. This could also shed some light on the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

By employing the stochastic extension of the Madelung quantum-hydrodynamic description within a discrete methodology, we establish a solution using the path integral approach to explore the progression of quantum states' superposition. This investigation aims to understand the eventual establishment of a stable end-state configuration amid the backdrop of gravitational background fluctuations. The model identifies the circumstances that lead to a limited range of interaction for the quantum potential, allowing for the emergence of sizeable, classically described macroscopic phenomena. The theory unveils the lowest achievable level of uncertainty in an open quantum system and investigate its congruence with the localized behaviors of macroscopic classical systems. The study examines agreements and differences with decoherence theory and the Copenhagen interpretation of quantum mechanics, and evaluates the impact of wave function decay on the measurement process.

When two black holes form a binary system, each black hole observes an event horizon and a curved distorted space-time region around the other black hole. In this space-time, two such regions are formed, and another black hole forms in the second region from the initial black hole, which may be termed the “image” of the first black hole. The same event occurs for the other black hole also, and an extra image of it is formed. In these conditions, the energy of the system divides between the two black holes and their images. These four new black holes that are formed interact with each other again and produce new horizons and new distorted regions. Each black hole produces an image of all the other black holes and detects the background of six black holes instead of three. Consequently, for four black holes, 24 new black holes arise. The energy of the system will be divided amongst all 24 black holes. This story continues and black holes interact with one another and produce new images. Finally, very light black holes are formed each of which is so weak that it cannot produce strong distortions of space-time. The radiated gravitational waves from these weak black holes could be detected by LIGO as well as the signature of these binary black holes. However, detected waves are only a part of very strong gravitational waves. Each time a part of these waves escapes from the system and reaches the earth, they may be regarded as emitted waves from a new binary black hole. The time between radiated signals decreases, and it may be interpreted that a new supermassive binary black hole is radiating. If radiated signals combine, an explosion of the very strong binary system could be detected.

A cosmological model described by the perturbation metric is proposed, in which space is entrained by matter expanding as a result of the Big Bang. In the absence of an input of external energy and momentum, the solution of the Einstein equations assumes a pressure equal to zero and an accelerated expansion. The cosmological perturbation model explains the difference in measurements of the Hubble constant using gravitational lensing and a distance ladder.

This short paper briefly explores the interplay between quantum mechanics and gravity, drawing from the principle of gravitational redshift and bringing it into quantum mechanical frameworks. The exploration looks through quantum mechanical relations and equations such as Planck-Einstein relation, De-Broglie’s relation and the relativistic wave equations, and propagators, accounting for the presence of gravitational fields through gravitational redshift of its momentum.

In the context of the minimally extended varying speed of light (meVSL) model, both the absolute magnitude and the luminosity distance of type Ia supernovae (SNe Ia) differ from those predicted by general relativity (GR). Utilizing the Pantheon+ data, we examine the plausibility of various dark energy models under meVSL. Both ωCDM and CPL parameterization dark energy (DE) models exhibit indications of cosmic variations in the speed of light at the 1-σ level. For Ωm0=0.30,0.31, and 0.32 with (ω0,ωa)=(−1,0), the 1-σ range of c˜˙0/c˜0(10−13yr−1) is (-8.76 , -0.89), (-11.8 , 3.93), and (-14.8 , -6.98), respectively. Meanwhile, the 1-σ range of c˜˙0/c˜0(10−12yr−1) for CPL dark energy models with −1.05≤ω0≤−0.95 and 0.28≤Ωm0≤0.32, is (-6.31 , -2.98). The value of c˜ at z=3 can exceed that of the present by 0.2∼3 % for ωCDM models and 5∼13 % for CPL models. Additionally, for viable models except for the CPL model with Ωm0=0.28, we find −25.6≤G˜˙0/G˜0(10−12yr−1)≤−0.36. For this particular model, we obtain an increasing rate of the gravitational constant within the range 1.65≤G˜˙0/G˜0(10−12yr−1)≤3.79.