Abstract
This chapter introduces the basic solutions of Einstein field equations that describe black holes. Motion of particles in the vicinity of black holes, space-time structure, and other elemental properties of each solution are discussed. Brief discussions are also presented on mini-black holes, Born-Infeld black holes, f(R) black holes, and regular black holes.
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Notes
- 1.
Asymptotic flatness is a property of the geometry of space-time which means that in appropriate coordinates, the limit of the metric at infinity approaches the metric of the flat (Minkowskian) space-time.
- 2.
Notice that dv loc/dτ=(dv loc/dr)(dr/dτ)=(dv loc/dr)v loc=r g c 2/r 2.
- 3.
We remind that two geometries are conformally equivalent if there exists a conformal transformation (an angle-preserving transformation) that maps one geometry to the other. More generally, two (pseudo) Riemannian metrics on a manifold M are conformally equivalent if one is obtained from the other through multiplication by a function on M.
- 4.
The relation with Boyer-Lindquist coordinates is z=rcosθ, \(x=\sqrt{r^{2}+a^{2}c^{-2}} \sin\theta\cos\phi\), \(y=\sqrt{r^{2}+a^{2}c^{-2}} \sin\theta\sin\phi\).
- 5.
\(F(\gamma, k)=\int_{0}^{\gamma}(1-k^{2}\sin^{2}\phi )^{-1/2}d\phi=\int_{0}^{\sin\gamma }[(1-z^{2})(1-k^{2}z^{2})]^{-1/2}dz \).
References
M.A. Abramowicz, A.M. Beloborodov, X.-M. Chen, I.V. Igumenshchev, Astron. Astrophys. 313, 334 (1996)
M. Born, L. Infeld, Proc. R. Soc. Lond. A 144, 425 (1934)
N. Bretón, Class. Quantum Gravity 19, 601 (2002)
S. Carroll, Space-Time and Geometry: An Introduction to General Relativity (Addison-Wesley, New York, 2003)
B. Carter, in Les Astres Occlus, ed. by C.M. DeWitt (Gordon and Breach, New York, 1973)
J.A.R. Cembranos, A. de la Cruz-Dombriz, P. Jimeno Romero, arXiv:1109.4519 (2011)
V.P. Frolov, I.D. Novikov, Black Hole Physics (Kluwer, Dordrecht, 1998)
V.P. Frolov, A. Zelnikov, Introduction to Back Hole Physics (Oxford University Press, Oxford, 2011)
V.P. Frolov, M.A. Markov, V.F. Mukhanov, Phys. Rev. D 41, 383 (1990)
S.W. Hawking, G.F.R. Ellis, The Large-Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973)
B. Hoffmann, Phys. Rev. 47, 877 (1935)
R.P. Kerr, Phys. Rev. Lett. 11, 237 (1963)
P.-S. Laplace, Exposition du Système du Monde, Paris. (first edition) (1796)
J.-P. Luminet, in Black Holes: Theory and Observation, ed. by F.W. Hehl, C. Kiefer, R.J.K. Metzler (Springer, Berlin, 1998), p. 3
V.S. Manko, N.R. Sibgatullin, Phys. Rev. D 46, R4122 (1992)
J. Michell, Philos. Trans. R. Soc. Lond. 74, 35 (1784)
M.R. Mbonye, D. Kazanas, Phys. Rev. D 72, 024016 (2005)
M.R. Mbonye, N. Battista, R. Farr, Int. J. Mod. Phys. D 20, 1 (2011)
E.T. Newman, E. Couch, K. Chinnapared, A. Exton, A. Prakash, R. Torrence, J. Math. Phys. 6, 918 (1965)
B. Paczyński, P. Wiita, Astron. Astrophys. 88, 23 (1980)
C.L. Pekeris, K. Frankowski, Phys. Rev. A 36, 5118 (1987)
R. Penrose, Riv. Nuovo Cimento I, 252 (1969)
D. Pérez, G.E. Romero, C.A. Correa, S.E. Perez-Bergliaffa, Int. J. Mod. Phys. Conf. Ser. 3, 396 (2011)
D. Pérez, G.E. Romero, S.E. Perez-Bergliaffa, Astron. Astrophys. 551, A4 (2013)
S.E. Perez-Bergliaffa, Y.E. Chifarelli de Oliveira Nunes, Phys. Rev. D 84, 084006 (2011)
B. Punsly, Astrophys. J. 498, 640 (1998a)
B. Punsly, Astrophys. J. 498, 660 (1998b)
B. Punsly, Black Hole Gravitohydromagnetics (Springer, Berlin, 2001)
B. Punsly, G.E. Romero, D.F. Torres, J.A. Combi, Astron. Astrophys. 364, 552 (2000)
D. Raine, E. Thomas, Black Holes: An Introduction (Imperial College Press, London, 2005)
O. Semerák, V. Karas, Astron. Astrophys. 343, 325 (1999)
P.K. Townsend, Black Holes (Lecture Notes) (University of Cambridge, Cambridge, 1997). arXiv:gr-qc/9707012
R.M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984)
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Romero, G.E., Vila, G.S. (2014). Black Holes. In: Introduction to Black Hole Astrophysics. Lecture Notes in Physics, vol 876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39596-3_2
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