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.
KeywordsBlack HolesEvent HorizonSchwarzschild MetricSingularityGeneral Theory of RelativityDark MatterNeutron Stars
Schwarzschild, K. (1916) über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie Wissenschaften, Berlin, 189. https://www.arxiv-vanity.com/papers/0709.2257/
Blinn, C. (2017) Schwarzschild Solution to Einstein’s General Relativity. Schwarzschild Solution. https://sites.math.washington.edu
Einstein, A. and Rosen N. (1935) The Particle Problem in the General Theory of Relativity. Physical Review, 48, 73-77. https://doi.org/10.1103/PhysRev.48.73
Kruskal, M. (1960) Maximal Extension of Schwarzschild Metric. Physical Review, 119, 1743-1745. https://doi.org/10.1103/PhysRev.119.1743 https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743
Rylov, Y. (1961) Singularity in the Schwarzschild Solution of the Gravitation Equations. Journal of Experimental and Theoretical Physics, 13, 1235-1236.
Fomin, P. (1968) Coordinate Transformations that Eliminate Singularities on the Gravitational Radius in the Schwarzschild Metric. Journal of Experimental and Theoretical Physics, 27, 483-485.
Bel, L. (1969) Schwarzschild Singularity. Journal of Mathematical Physics, 10, 1501-1503. https://doi.org/10.1063/1.1664997 https://aip.scitation.org/doi/10.1063/1.1664997
Janis, A., Newman, E. and Winicour, J. (1968) Reality of the Schwarzschild Singularity. Physical Review Letters, 20, 878-880. https://doi.org/10.1103/PhysRevLett.20.878 https://journals.aps.org/prl/
Schiffer, M, Adler, R., Mark, J. and Shiffield, C. (1973) Kerr Geometry as Complexified Schwarzschild Geometry. Journal of Mathematical Physics, 14, 52-56. https://doi.org/10.1063/1.1666171
Martel, K. and Poisson, E. (2000) Regular Coordinate Systems for Schwarzschild and Other Spherical Spacetimes. The American Association of Physics Teachers, 69, 476-480. https://doi.org/10.1119/1.1336836
Casana, R., Canvalcante, A., Poulis, F., and Snatos E. (2018) Exact Schwarzschild-Like Solution in a Bumblebee Gravity Model. Physical Review D, 97, Article ID: 104001. https://doi.org/10.1103/PhysRevD.97.104001
Chemisana, D., Gine, J. and Madrid, J. (2021) Generalized Dirac Equation for a Particle in a Gravitational Field. General Relativity and Gravitation, 53, Article No. 65. https://doi.org/10.1007/s10714-021-02834-y
Einstein, A. (1939) On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses. Annals of Mathematics, 40, 922-936. https://doi.org/10.2307/1968902
Tolman, R. (1939) Static Solutions of Einstein’s Field Equations for Spheres of Fluid. Physical Review, 55, 364-373. https://doi.org/10.1103/PhysRev.55.364 https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364
Oppenheimer, J. and Snyder, H (1939) On Continued Gravitational Contraction. Physical Review, 56, 455-459. https://doi.org/10.1103/PhysRev.56.455 https://journals.aps.org/pr/abstract/10.1103/PhysRev.56.455
Abramowicz, M. and Prasanna, A. (1990) Centrifugal-Force Reversal Near a Schwarzschild Black Hole. Monthly Notices of the Royal Astronomical Society, 245, 720-728. http://adsabs.harvard.edu/pdf/1990MNRAS.245.720A
Synge, J.L. (1949) The Gravitational Field of a Particle. Nature, 164, 148-149. https://doi.org/10.1038/164148b0 https://www.jstor.org/stable/20488511
Lemaitre, G. (1949) Cosmological Application of Relativity. Review of Modern Physics, 21, 357-366. https://doi.org/10.1103/RevModPhys.21.357 https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.21.357
Raychaudhuri, A. (1953) Arbitrary Concentrations of Matter and the Schwarzschild Singularity. Physical Review, 89, 417-421. https://doi.org/10.1103/PhysRev.89.417
Einstein, A. (1930) The Meaning of Relativity. 4th Edition, Methuen and Company, Ltd., London, 113.
Regge, T. and Wheeler, J. (1957) Stability of a Schwarzschild Singularity. Physical Review, 108, 1063-1069. https://doi.org/10.1103/PhysRev.108.1063 https://journals.aps.org/pr/abstract/10.1103/PhysRev.108.1063
Fronsdal, C. (1959) Completion and Embedding of the Schwarzschild Solution. Physical Review, 116, 778-781. https://doi.org/10.1103/PhysRev.116.778 https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.778
Duff, M. (1974) Quantum Corrections to the Schwarzschild Solution. Physical Review D, 9, 1837-1839. https://doi.org/10.1103/PhysRevD.9.1837 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.9.1837
Dadhich, N. (1997) On the Schwarzschild Field. arXiv: gr-qc/9704068.
Doran, R., Crawford, P. and Lobo F. (2008) Interior of a Schwarzschild Black Hole Revisited. Foundations of Physics, 38, 160-187. https://doi.org/10.1007/s10701-007-9197-6
Turimov, B. and Ahmedov, B. (2021) Zipoy-Voorhees Gravitational Object as a Source of High-Energy Relativistic Particles. Galaxies, 9, Article No. 59. https://doi.org/10.3390/galaxies9030059
Kofinti, N. (1984) On a New Interior Schwarzschild Solution. General Relativity and Gravitation, 17, 245-249. https://doi.org/10.1007/BF00760246
Dimnikova, I. (1996) The Sitter-Schwarzschild Black Hole: Its Particlelike Core and Thermodynamic Properties. International Journal of Modern Physics D, 5, 529-540. https://doi.org/10.1142/S0218271896000333
Chaichian, M., Tureanu, A., and Zet, G. (2008) Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity. Physics Letter B, 660, 573-578. https://doi.org/10.1016/j.physletb.2008.01.029
Einstein, A. (1916) Hamilton’s Principle and the General Theory of Relativity. 2015 English Translation, Princeton University Press, Princeton.
D’addio, A. (2021) S-Star Dynamics through a Yukawa-Like Gravitational Potential. Physics of the Dark Universe, 33, Article ID: 100871. https://doi.org/10.1016/j.dark.2021.100871
Oppenheimer, J. and Volkoff, G. (1939) On Massive Neutron Cores. Physical Review Journals Archive, 55, 374-381. https://doi.org/10.1103/PhysRev.55.374
Abuter, R., Amorim, A., Anugu, N., Bauböck, M., Benisty, M., Berger, J.P., et al. (2019) Detection of the Gravitational Redshift in the Orbit of the Star S2 Near the Galactic Centre Massive Black Hole. Astronomy & Astrophysics, 615, Article No. L15. https://doi.org/10.1051/0004-6361/201833718 http://hdl.handle.net/10871/35577
Sofue, Y. (2013) Rotation Curve and Mass Distribution in the Galactic Center. From Black Hole to Entire Galaxy. Astronomical Society of Japan, 65, Article No. 118. https://doi.org/10.1093/pasj/65.6.118
Parra J., (2021) Photonic Gravitational Interactions from a Quantum Point of View. Optics and Photonics Journal, 11, 12-21. https://doi.org/10.4236/opj.2021.111002 https://www.scirp.org/pdf/opj