Abstract
We review here the basic setup to describe complete gravitational collapse of massive bodies within the general theory of relativity. We derive Einstein’s equations describing collapse and solve them in some simple well-known toy models. We study the final outcome of collapse and the quantities that describe the formation of trapped surfaces and of the central singularity.
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References
C. Bambi, Phys. Rev. D 87, 023007 (2013)
C. Bambi, D. Malafarina, Phys. Rev. D 88, 064022 (2013)
C. Bambi, D. Malafarina, L. Modesto, Phys. Rev. D 88, 044009 (2013)
M. Bojowald, R. Goswami, R. Maartens, P. Singh, Phys. Rev. Lett. 95, 091302 (2005)
K. Bolejko, A. Krasiński, C. Hellaby, M.N. Celerier, Structures in the Universe by Exact Methods: Formation, Evolution, Interactions, sect. 18 (Cambridge University Press, Cambridge, 2010)
H. Bondi, Mon. Not. Astron. Soc. 107, 343 (1947)
I. Booth, Can. J. Phys. 83, 1073 (2005)
S. Chandrasekhar, Asrophys. J. 74, 81 (1931)
D. Christodoulou, Commun. Math. Phys. 93, 171 (1984)
M. Colpi, S.L. Shapiro, I. Wasserman, Phys. Rev. Lett. 57, 2485–2488 (1986)
S. Datt, Zs. F. Phys. 108, 314 (1938)
D.M. Eardley, L. Smarr, Phys. Rev. D 19, 2239 (1979)
F. Fayos, X. Jaen, E. Llanta, J.M.M. Senovilla, Phys. Rev. D 45, 2732 (1992)
F. Fayos, J.M.M. Senovilla, R. Torres, Phys. Rev. D 54, 4862 (1996)
D. Finkelstein, Phys. Rev. 110, 965 (1958)
B. Freedman, L.D. McLerran, Phys. Rev. D 17, 11091122 (1978)
R. Goswami, P.S. Joshi, P. Singh, Phys. Rev. Lett. 96, 031302 (2006)
S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973)
S.W. Hawking, R. Penrose, Proc. R. Soc. Lond. A 314, 529 (1970)
S.A. Hayward, Phys. Rev. D 49, 6467 (1994)
C. Hellaby, K. Lake, Astrophys. J. 290, 381 (1985)
C. Hellaby, K. Lake, Astrophys. J. 300, 461 (1986)
W. Israel, Nuovo Cimento B 44, 1 (1966); Nuovo Cimento B 48, 463 (1966)
H.T. Janka, Annu. Rev. Nucl. Part. Sci. 62(1), 407 (2012)
H.T. Janka, F. Hanke, L. Hdepohl, A. Marek, B. Mller, M. Obergaulinger, Prog. Theor. Exp. Phys. 2012(1), id.01A309 (2012)
P.S. Joshi, I.H. Dwivedi, Phys. Rev. D 47, 5357 (1993)
P.S. Joshi, I.H. Dwivedi, Class. Quantum Gravity 16, 41 (1999)
P.S. Joshi, D. Malafarina, Int. J. Mod. Phys. D 20(14), 2641 (2011)
P.S. Joshi, D. Malafarina, R. Narayan, Class. Quantum Gravity 28, 235018 (2011)
P.S. Joshi, D. Malafarina, R. Narayan, Class. Quantum Gravity 31, 015002 (2014)
A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, 1997)
A. Krasinski, J. Plebanski, Introduction to General Relativity and Cosmology, sect. 18.15 (Cambridge University Press, Cambridge, 2006), pp. 301
G. Lemaìtre, Ann. Soc. Sci. Bruxelles I, A 53, 51 (1933)
P.O. Mazur, E. Mottola (2001), arXiv:0109035 [gr-qc]
C. Misner, D. Sharp, Phys. Rev. 136, B571 (1964)
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W. H Freeman, San Francisco, 1973)
R.P.A.C. Newman, Class. Quantum Gravity 3, 527 (1986)
J.R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939)
J.R. Oppenheimer, G.M. Volkov, Phys. Rev. 56, 374 (1939)
R. Penrose, Phys. Rev. Lett. 14, 57 (1965)
R. Penrose, Rivista del Nuovo Cimento 1, 257 (1969)
L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, M.A. Aloy, Astrophys. J. Lett. 732, L6 (2011)
R.C. Tolman, Proc. Natl. Acad. Sci. USA 20, 410 (1934)
R.C. Tolman, Phys. Rev. 55, 364 (1939)
D.F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D 62, 104012 (2000)
M. Visser, C. Barcelo, S. Liberati, S. Sonego (2009), arXiv:0902.0346 [gr-qc]
R.M. Wald, General Relavitity, sect. 6.2 (University of Chicago Press, Chicago, 1984), p. 125
B. Waugh, K. Lake, Phys. Rev. D 38, 1315 (1988)
P. Yodzis, H.-J. Seifert, H. Muller zum Hagen, Commun. Math. Phys. 34, 135 (1973)
J.B. Zeldovich, L.F. Grishchuk, Mon. Not. R. Astron. Soc. 2(07), 23 (1984)
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Malafarina, D. (2016). A Brief Review of Relativistic Gravitational Collapse. In: Bambi, C. (eds) Astrophysics of Black Holes. Astrophysics and Space Science Library, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52859-4_5
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