Simple Analytic Models of Gravitational Collapse

Details Simple Analytic Models of Gravitational Collapse Simple Analytic Models of Gravitational Collapse

2005-02-09

arxiv.org/abs/gr-qc/0502040v1

Am.J.Phys. 73 (2005) 1148-1159

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to American Journal of Physics

Scientific paper

10.1119/1.2117187

Most general relativity textbooks devote considerable space to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. However only a few discuss the dynamical process of gravitational collapse, by which black holes and singularities form. We present here two types of analytic models for this process, which we believe are the simplest available; the first involves collapsing spherical shells of light, analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is pedagogical simplicity and algebraic completeness, but we also present some results that we believe are new, such as the collapse of a light shell in Kruskal-Szekeres coordinates.

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