Simple analytical models of gravitational collapse

2005/02/09 by R. J. Adler, Ronald J. Adler, J. D. Bjorken +4 · 1 voice · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #astro-ph #gr-qc

paper · pdf · doi:10.1119/1.2117187

published as Am.J.Phys. 73 (2005) 1148-1159 · Submitted to American Journal of Physics

arxiv created 2005/02/09 · arxiv published 2005/02/09 · openalex publication_date 2005/11/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Most general relativity textbooks devote considerable attention to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. Only a few discuss the dynamical process of gravitational collapse by which black holes and singularities form. We present two simple analytical models that describe this process. The first involves collapsing spherical shells of light and is analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid and is analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is simplicity and algebraic completeness, but we also present a few more sophisticated results such as the collapse of a light shell in Kruskal-Szekeres coordinates.

Citations

• On the singularities of a Riemannian manifold
• The Generalized Uncertainty Principle and Black Hole Remnants
• A First Course in General Relativity
• Particle creation by black holes
• Hawking Radiation as Tunneling
• On Continued Gravitational Contraction

Cited by

• An analytic model for gravitational collapse of spherical matter under mixed pressure
• Evolving black hole horizons in General Relativity and alternative gravity
• Classicalization of gravitons and Goldstones

Discussions

• First of all, “a black hole that emits radiation” should properly be called a white hole . Second, no, the proposed metric cannot be thought as corresponding to a white hole radiating massive particle [stackexchange, 3 points]