Geodesic
Before getting around to do black hole physics...
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 147-184

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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.
Keywords: General Relativity, spherical gravity, thin shells, Schwarzschild manifold, Vaidya metrics. 
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     author = {V. A. Berezin},
     title = {Before getting around to do black hole physics...},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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     number = {3},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a13/}
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V. A. Berezin. Before getting around to do black hole physics.... Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 147-184. http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a13/