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Twin Paradox and Proper Time

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Journal of Applied Mathematics and Physics 2024年第1期12卷 12-15页

作者： Donald Lem White Plains NY USA

Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a much deeper understanding … of the theory of relativity”. The deeper understanding of resolving the paradox is by applying more explicit definitions of proper time interval, Lorentz transform, time dilation, and aging time.

关键词： Twin Paradox Proper Time Minkowski metric schwarzschild metric

schwarzschild Quantum Light Geodesics metric: A Pair of BH-Inner WH

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Journal of High Energy Physics, Gravitation and Cosmology 2021年第3期7卷 1089-1101页

作者： Jean Perron Department of Applied Sciences Université du Québec à Chicoutimi Chicoutimi Canada

In this article we hypothesized that the arrow of time and space evolve in a discontinuous way in the form of quanta (t=ntp, s=mlp). We applied this reasoning to the light geodesics of schwarzschild’s metric (dsmin=lp) and obtained different characteristics of the BH. Indeed, quantum light geodesics show that inside the BH a WH is formed and the mass (energy) is not directing towards the singularity r→0 but rather around the BH near the EH as a thick skin (tickness ). The total relativistic energy invariant is satisfied for the entire route of the photons. Subsequently, as mass (energy) is found directly at the EH, we applied the quantum tunnel effect in simple semi-classical analysis, and we obtained that particles like protons can leave the EH and that the energy associated with them is in the order of magnitude of Hawking’s radiation. However, the energy of the protons is not necessarily identified with that of the black body (photonic or electromagnetic). Finally, it would be interesting to see the impacts of this quantum light geodesics (dsmin=lp) on other cases like Kerr’s metric.

关键词： Black Hole White Hole schwarzschild metric Quantum Spacetime Tunnel Effect

Time-Like Geodesic Motion in schwarzschild Spacetime with Weak-Field Limit

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Chinese Physics Letters 2015年第8期32卷 27-29页

作者：张软静陈菊华甘俏姗王永久 College of Physics and Information Science Hunan Normal University

We analyze the geodesic motion in schwarzschild spacetime with the weak-field limit. We investigate all geodesic types of the test particle by solving the geodesic equation and analyzing the behavior of effective potential. At the same time, all kinds of orbits, which are allowed according to the energy level corresponding to the effective potential, are numerically simulated in detail. Then we discuss the effect of different parameters on the effective potential energy. We also find that the test particle falls rapidly along the fall-into orbit and the radius of stable （unstable） circular orbits become larger in the schwarzschild spacetime with the weak-field limit than those in the schwarzschild case.

关键词： GEODESIC motion schwarzschild metric EQUATIONS of motion ENERGY levels (Quantum mechanics) GENERAL relativity (Physics)

Local Stability to the Einstein-Euler System in schwarzschild Space-time

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Acta Mathematicae Applicatae Sinica 2022年第2期38卷 352-367页

作者： Jun WU Bo-ling GUO Institute of Applied Physics and Computational Mathematics Beijing 100088China

We study the schwarzschild spacetime solutions to the Einstein-Euler *** our analysis,we aim to show local stability under small *** resolve this problem,we use the Nash-Moser(-Hamilton)*** work was originally develop... 详细信息

关键词： schwarzschild metric local stability Nash-Moser(-Hamilton)theorem

Direct and Exact Description of Null Geodesics in schwarzschild Spacetime

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Journal of High Energy Physics, Gravitation and Cosmology 2023年第1期9卷 234-244页

作者： Leo Morgovsky Johann Wolfgang Goethe-Universitä t Frankfurt am Main Frankfurt Germany

Null geodesics for massless particles in schwarzschild spacetime are obtained by direct integration of the trajectory equation in spatial coordinates without transformation to the inverse space. The results are classified following Chandrasekhar depending on the ratio of the impact parameter of the trajectory to its critical value. In the subcritical and supercritical cases the geodesics are expressed in terms of elliptic integrals of the first kind. Some results are formally different from the classical ones, but in fact equivalent to them, being at the same time more compact and descriptive.

关键词： Black Holes schwarzschild metric Photon Trajectory Hawking Radiation

A Mathematical Comparison of the schwarzschild and Kerr metrics

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Journal of Modern Physics 2020年第10期11卷 1672-1710页

作者： J.-F. Pommaret CERMICS Ecole des Ponts ParisTech Paris France

A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M), schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well known for M, but also third order CC for S and K. In a recent paper (DOI:10.4236/jmp.2018.910125) we have studied the cases of M and S, without using specific technical tools such as Teukolski scalars or Killing-Yano tensors. However, even if S(m) and K(m, a) are depending on constant parameters in such a way that S → M when m → 0 and K→ S when a → 0, the CC of S do not provide the CC of M when m → 0 while the CC of K do not provide the CC of S when a → 0. In this paper, using tricky motivating examples of operators with constant or variable parameters, we explain why the CC are depending on the choice of the parameters. In particular, the only purely intrinsic objects that can be defined, namely the extension modules, may change drastically. As the algebroid bracket is compatible with the

关键词： Formal Integrability Involutivity Compatibility Condition Janet Sequence Spencer Sequence Minkowski metric schwarzschild metric Kerr metric

The properties and geodesics related to the NUT-Taub-like spacetime

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Chinese Physics B 2006年第5期15卷 927-933页

作者：吴亚波赵国明邓雪梅杨秀一吕剑波李松 Department of Physics Liaoning Normal University Dalian 116029 China

Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊〈〈 M, respectively.

关键词： NUT-Taub spacetime schwarzschild metric geodesics

Encoding Energy-Density as Geometry

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Journal of Modern Physics 2021年第9期12卷 1190-1209页

作者： Edwin Eugene Klingman Cybernetic Micro Systems Inc. San Gregorio CA USA

Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support the “time-dilation” interpretation and others support “curved space-time” interpretation. In this, and related work, we investigate the key issues in terms of the intuitive space-time frame. In particular, we provide alternative approaches to explain “time dilation” and to explain the energy density for gravity systems. We approach the latter problem from an information perspective.

关键词： Curved Space-Time Gravitational Energy Stress-Energy Tensor Encoding Information in Geometry Time Dilation Equivalence Principle Minkowski Relation schwarzschild metric Linearized General Relativity Cosmology

<i>D’addio</i>to Blackness

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International Journal of Astronomy and Astrophysics 2021年第4期11卷 509-516页

作者： Jose L. Parra Department of Physics Florida International University Miami USA

It is assumed here that the energy of a strong gravitational field creates non-linear effects over enclosed masses. This idea and the rigorous rules of the General Theory of Relativity output a metric that covers strong and weak gravitational fields. The proposed metric could be correct because it included the schwarzschild’s metric as a particular case and has no singularities. Additionally, it appears here that the massive condition of the gravitational fields has properties like the so-called Dark Matter.

关键词： Black Holes Event Horizon schwarzschild metric Singularity General Theory of Relativity Dark Matter Neutron Stars