This is a short note on a new way to describe Haug's newly introduced maximum velocity for matter in relation to the Schwarzschild radius. This leads to a probabilistic Schwarzschild radius for elementary particles with mass smaller than the Planck mass. In addition, our maximum velocity, when linked to the Schwarzschild radius, seems to predict that particles just at that radius cannot move. This implies that radiation from the Schwarzschild radius not can undergo velocity time dilation. Our maximum velocity of matter, therefore, seems to predict no time dilation, even in high Z quasars, as has surprisingly been observed recently.

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.

This paper proposes a relativistic model of the Universe in which the geometry describes a 4D version of the 2-sheeted hyperboloid that is isotropic, homogeneous in space at a given time and inhomogeneous in time. The radius of this metric is temporal as opposed to spatial. It predicts both a Universe and Anti-Universe moving in opposite directions of time undergoing an expansion phase, followed by a collapsing phase. Using only the current age of the Universe and transition redshift, it predicts the accelerated expansion and it is shown that its Hubble diagram fits currently available supernova and quasar data as well as predicting a Hubble constant $H_0\approx71.6km/s/Mpc$. The angular term of the metric describes time dilation caused by the relativistic kinematic precession effect known as Thomas Precession which can be interpreted as spin about the time dimension. The model also makes two novel predictions: that the early Universe should have structures older than expected due to an increased amount of proper time relative to coordinate time in that era and that the background Universe should appear brighter than current models predict.

The Schwarzschild metric describes a non-rotating and charge-free celestial body, and it results in things stopping at the event horizon of a black hole and spending infinite time across the event horizon by the observer far away from the black hole. The analysis of the particle’s behavior at the event horizon tells us that this solution predicts an un-expanded black hole which violates the astronomical observations and our knowledge about the black hole. Although some alternative metrics have been proposed, the singularity problem is still unsolved. In this research, the degenerate Fermi electron gas is used to reveal that the Fermi electron gas cannot shrink to a point no matter how large energy it obtains, so the singularity exists at the center very unreasonably. In order to avoid these problems, a finite-size nucleus of the black hole is proposed and reasonably explained by the behaviors of the Fermi electron gas and the Fermi neutron gas there. On the other hand, the Kerr-Newman metric is the one describing the rotating and charged black hole and the equation of the light velocity at each space point can be obtained. It tells us that there are two real and non-imaginary solutions for the radial speed of light at the position larger than the Schwarzschild radius.

General wisdom thinks that the central of blackholes are singular and featured by mass, charge and spin exclusively; the microstate reflected in the Bekenstein-Hawking entropy can be accounted for only in some quantum gravity. We challenge this wisdom with two exact solution families to the sourceful Einstein equation which describe dust ball with oscillatory inner structure and variety of mass profiles. We attribute the matter content's oscillation across the central point of the system to the forward scattering domination in high energy collisions induced by inter-gravitating acceleration and provide their Penrose-Carter diagram representation and quantum description briefly. Our solution family provides a very simple semi-classic picture for the micorstate definition of black holes.

In modern physics, it is assumed that the Planck length is a derived constant from Newton's gravitational constant, the Planck constant and the speed of light, $l_p=\sqrt{\frac{G\hbar}{c^3}}$. This was first discovered by Max Planck in 1899. We suggest a way to find the Planck length independent of any knowledge of Newton's gravitational constant or the Planck constant, but still dependent on the speed of light (directly or indirectly).

In this paper we show that the Schwarzschild radius can be extracted easily from any gravitationally-linked phenomena without having knowledge of the Newton gravitational constant or the mass size of the gravitational object. Further, the Schwarzschild radius can be used to predict any gravity phenomena accurately, again without knowledge of the Newton gravitational constant and also without knowledge of the size of the mass, although this may seem surprising at first. Hidden within the Schwarzschild radius are the mass of the gravitational object, the Planck mass (their relative mass), and the Planck length. We do not claim to have all the answers, but this seems to indicate that gravity is quantized, even at a cosmological scale, and this quantization is directly linked to the Planck units. This also supports our view that the Newton gravitational constant is a universal composite constant of the form $G=\frac{l_p^2{c}^3}{\hslash }$ , rather than relying on the Planck units as a function of G. This does not mean that Newton’s gravitational constant is not a universal constant, but that it is instead a composite universal constant that depends on the Planck length, the speed of light, and the Planck constant. Further, $\frac{G\times 1\hspace{0.17em}\mathrm{weight}\hspace{0.17em}\mathrm{unit}}{c^2}=\frac{G}{c^2}$ is the Schwarzschild radius off one weight unit. So G is only needed when we want to use gravity to find the weight of an object, such as weighing the Earth. This is, to our knowledge, the first paper that shows how a long series of major gravity predictions and measurements can be completed without any knowledge of the mass size of the object, or Newton’s gravitational constant. As a minimum we think it provides an interesting new angle for evaluating existing gravity theories, and it may even give us a small hint on how to combine quantum gravity with Newton and Einstein gravity.

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.

Recent experimental research has shown that mass is linked to Compton periodicity. We suggest a new way to look at mass: Namely that mass at its most fundamental level can simply be seen as reduced Compton frequency over the Planck time. In this way, surprisingly, neither the Planck constant nor Newton's gravitational constant are needed to observe the Planck length, nor in any type of calculation or gravitational predictions. The Planck constant is only needed when we want to convert back to the more traditional and we would say arbitrary mass measures such as kg. The theory gives the same predictions as Einstein's special relativity theory, with one very important exception: anything with mass must have a maximum velocity that is a function of the Planck length and the reduced Compton wavelength. For all observed subatomic particles, such as the electron, this velocity is considerably above what is achieved in particle accelerators, but always below the speed of light. This removes a series of infinity challenges in physics. The theory also offers a way to look at a new type of quantum probabilities. As we will show, a long series of equations become simplied in this way. Further Newton's gravitational constant G is clearly not needed for gravity calculations or predictions; it is the Planck length and the speed of light (gravity) that are essential for gravity, and both can be measured easily with no knowledge of G.

A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.

The subject of this paper is to analyse the Math Principia of Economic 3D Black Holes in Roegenian economics. This idea is totally new in the related literature, excepting our papers. In details, we study two special problems: (i) math origin of economic 3D black holes, (ii) entropy and internal political stability depending on national income and the total investment, for economic RN 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach so different), to complete the thermodynamics-economics dictionary with new entities, to introduce the flow between two macroeconomic systems, to study the Schwarzschild type metric properties on an economic 4D system, together with Rindler coordinates, Einstein 4D PDEs, and economic RN 3D black hole. In addition, we introduce some economic Ricci type flows or waves, for further research.

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.

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.

There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, `wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of `principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new `tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a `tensor observable' of spacetime.