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.
References
[1]
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/
[2]
Blinn, C. (2017) Schwarzschild Solution to Einstein’s General Relativity. Schwarzschild Solution. https://sites.math.washington.edu
[3]
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
[4]
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
[5]
Rylov, Y. (1961) Singularity in the Schwarzschild Solution of the Gravitation Equations. Journal of Experimental and Theoretical Physics, 13, 1235-1236.
[6]
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.
[7]
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
[8]
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/
[9]
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
[10]
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
[11]
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
[12]
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
[13]
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
[14]
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
[15]
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
[16]
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
[17]
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
[18]
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
[19]
Raychaudhuri, A. (1953) Arbitrary Concentrations of Matter and the Schwarzschild Singularity. Physical Review, 89, 417-421. https://doi.org/10.1103/PhysRev.89.417
[20]
Einstein, A. (1930) The Meaning of Relativity. 4th Edition, Methuen and Company, Ltd., London, 113.
[21]
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
[22]
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
[23]
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
[24]
Dadhich, N. (1997) On the Schwarzschild Field. arXiv: gr-qc/9704068.
[25]
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
[26]
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
[27]
Kofinti, N. (1984) On a New Interior Schwarzschild Solution. General Relativity and Gravitation, 17, 245-249. https://doi.org/10.1007/BF00760246
[28]
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
[29]
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
[30]
Einstein, A. (1916) Hamilton’s Principle and the General Theory of Relativity. 2015 English Translation, Princeton University Press, Princeton.
[31]
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
[32]
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
[33]
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
[34]
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
[35]
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
