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EXACT SOLUTION FOR THE INTERIOR OF A BLACK HOLE

THEO M. NIEUWENHUIZEN

Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

https://doi.org/10.1142/S0219477508004441Cited by:0 (Source: Crossref)

Abstract

Within the Relativistic Theory of Gravitation it is shown that the equation of state p = ρ holds near the center of a black hole. For the stiff equation of state p = ρ − ρ_c the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range beyond the horizon. The solution is regular everywhere, with a specific shape at the origin. The gravitational redshift at the horizon remains finite but is large, z ~ 10²³ M_⊙/M. Time keeps its standard role also in the interior. The energy of the Schwarzschild metric, shown to be minus infinity in the General Theory of Relativity, is regularized in this setup, resulting in E = Mc².

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References

R. J. McLure and J. S. Dunlop, Mon. Not. Roy. Astron. Soc. 331, 795 (2002), DOI: 10.1046/j.1365-8711.2002.05236.x. Crossref, Web of Science, Google Scholar
J.-W. Lee, J. Lee and H.-C. Kim, Journ. Cosm. Astropart. Phys. 08, 005 (2007). Crossref, Google Scholar
A. A. Logunov , The Theory of Gravity ( Nauka , Moscow , 2001 ) , arXiv:gr-qc/0210005 . Google Scholar
S. S. Gershtein, A. A. Logunov and M. A. Mestvirishvili , arXiv:gr-qc/0602029 . Google Scholar
N. Rosen, Phys. Rev. 57 (1940) 147; [ibid. 150; Ann. Phys. 22 (1963) 11] . Google Scholar
S. Deser, Gen. Rel. and Grav. 1, 9 (1970), DOI: 10.1007/BF00759198. Crossref, Google Scholar
L. P. Grishchuk, A. N. Petrov and A. D. Popova, Comm. Math. Phys. 94, 379 (1984), DOI: 10.1007/BF01224832. Crossref, Web of Science, Google Scholar
Th. M. Nieuwenhuizen, Europhys. Lett. 78, 10010 (2007), DOI: 10.1209/0295-5075/78/10010. Crossref, Google Scholar
Y. B. Zel'dovich, JETP 14, 1143 (1962). Google Scholar
H. A. Buchdahl and W. J. Land, J. Austr. Math. Soc. 3, 6 (1968). Web of Science, Google Scholar
S. V. Babak and L. P. Grishchuk, Phys. Rev. D 61, 024038 (1999), DOI: 10.1103/PhysRevD.61.024038. Crossref, Web of Science, Google Scholar
P. O. Mazur and E. Mottola, Proc. Nat. Acad. Sci. 101, 9545 (2004), DOI: 10.1073/pnas.0402717101. Crossref, Web of Science, Google Scholar
A. N. Petrov, Found. Phys. Lett. 18, 477 (2005), DOI: 10.1007/s10702-005-7538-2. Crossref, Web of Science, Google Scholar