Two time-dependent mass profiles are proposed as exact models of the last stage of Schwarzschild collapse; one develops the curvature singularity immediately, the other only at infinite time, though the second model's formulas are internally inconsistent.
Simple Analytic Models of Gravitational Collapse
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abstract
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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gr-qc 1years
2024 1verdicts
REJECT 1representative citing papers
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Analytic models for gravitational collapse
Two time-dependent mass profiles are proposed as exact models of the last stage of Schwarzschild collapse; one develops the curvature singularity immediately, the other only at infinite time, though the second model's formulas are internally inconsistent.