Before getting around to do black hole physics...

V. A. Berezin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 147-184.

Résumé

The short history is presented of the very notion “black hole”. The global geometry of the general spherically symmetric space-time is described. Einstein equations for spherical gravity are derived. The causal structure of the Schwarzschild black hole is investigated, and it is shown in details how to construct conformal Carter–Penrose diagrams that reveal visually such a structure. The Israel equations for self-gravitating thin shells are obtained and the modified gravitational Newton's law is investigated. Very simple and instructive derivation of the Vaidya metrics describing the spherically symmetric gravitating radiation is given. As an application of the theory described above the problem of the real (not virtual) static Schwarzschild observer is solved.

Détail

Keywords: General Relativity, spherical gravity, thin shells, Schwarzschild manifold, Vaidya metrics.

Bibliographie

[1] J. Michell, “On the Means of Discovering the Distance, Magnitude, of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S. In a Letter to Henry Cavendish, Esq. F. R. S. and A. S.”, Phil. Trans. R. Soc., 74 (1784), 35–57 | DOI

[2] P.-S. Laplace, Le Système du Monde, v. II, Paris, 1799; P. S. Laplas, Izlozhenie sistemy mira, Nauka, L., 1982, 376 pp.

[3] A. Einstein, “Zur Elektrodynamik bewegter Körper”, Ann. der Phys. (4), 17 (1905), 891–925 pp. | DOI | Zbl

[4] A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Ann. der Phys. (4), 17 (1905), 132–148 | DOI | Zbl

[5] A. Einstein, “Zur Theorie der Lichterzeugung und Lichtabsorption”, Ann. der Phys. (4), 20 (1906), 199–206 | DOI | Zbl

[6] A. Einstein, “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?”, Ann. der Phys. (4), 18 (1905), 639–641 | DOI

[7] A. Einstein, “Über die vom Relativitätsprinzip geforderte Trägheit der Energie”, Ann. der Phys. (4), 23 (1907), 371–384 | DOI | Zbl

[8] K. Schwarzschild, On the gravitational field of a mass point according to Einstein's theory, arXiv: [physics.hist-ph] physics/9905030 | Zbl

[9] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, A Course of Theoretical Physics, 2, Pergamon Press, Oxford, 1971, xi+374 pp. | MR

[10] I. D. Novikov, “$R$- and $T$-regions in space-time with a spherically symmetrical space”, Soobsh. GAISh, 132:3 (1964), 3–42 | MR

[11] V. A. Berezin, V. A. Kuzmin, I. I. Tkachev, “Dynamics of bubbles in general relativity”, Phys. Rev. D, 36:10 (1987), 2919–2944 | DOI | MR

[12] V. A. Berezin, Vector-like Einstein's equations for D-dimensional spherical gravity with (D-2)-dimensional sphere, arXiv: gr-qc/0010083

[13] V. A. Berezin, A. L. Smirnov, “Crossing thin shells”, Grav. Cosmol., 9:4 (2003), 235–242 | MR | Zbl

[14] D. Finkelstein, “Past-Future Asymmetry of the Gravitational Field of a Point Particle”, Phys. Rev., 110:4 (1958), 965–967 | DOI | MR | Zbl

[15] G. D. Birkhoff, Relativity and Modern Physics, Harvard University Press, Cambridge, 1923 | Zbl

[16] J. A. Wheeler, “Our Universe: The Known and the Unknown”, Amer. Sch., 37:2 (1968), 248–274

[17] J. A. Wheeler, “Our Universe: The Known and the Unknown”, Am. Sci., 56:1 (1968), 1–20

[18] J. A. Wheeler, “Our Universe: The Known and the Unknown”, Phys. Teach., 7:1 (1968), 24–34 | DOI

[19] A. Einstein, N. Rosen, “The Particle Problem in the General Theory of Relativity”, Phys. Rev., 48:1 (1935), 73–77 | DOI | Zbl

[20] W. Israel, “Singular hypersurfaces and thin shells in general relativity”, Il Nuovo Cimento B Series 10, 44:1 (1966), 1–14 | DOI

[21] W. Israel, “Singular hypersurfaces and thin shells in general relativity”, Il Nuovo Cimento B Series 10, 48:2 (1967), 463 | DOI

[22] K. Kuchař, “Charged shells in general relativity and their gravitational collapse”, Czeck. J. Phys. B, 18:4 (1968), 435–463 | DOI

[23] V. Berezin, “Could a real (not virtual) static observer exist outside a Schwarzschild black hole?”, Gen. Rel. Grav., 44:6 (2012), 1555–1561, arXiv: [gr-qc] 1106.0670 | DOI | MR | Zbl