Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details

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SUMMARY

The Oppenheimer-Snyder model of gravitational collapse describes the dynamics of a spherically symmetric massive object, as originally presented in their 1939 paper. This discussion elaborates on the mathematical details of the model, utilizing a methodology inspired by MTW (Misner, Thorne, and Wheeler) and Landau & Lifschitz. A comparison is made with Weinberg's approach, which focuses on the exterior vacuum metric in standard Schwarzschild coordinates, highlighting the differences in methodology without delving into Weinberg's specifics.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with the Oppenheimer-Snyder model
  • Knowledge of Schwarzschild coordinates
  • Mathematical proficiency in tensor calculus
NEXT STEPS
  • Study the original Oppenheimer and Snyder 1939 paper on gravitational collapse
  • Explore the Misner, Thorne, and Wheeler (MTW) textbook for advanced gravitational theories
  • Investigate Landau & Lifschitz's approach to gravitational collapse
  • Learn about Weinberg's treatment of vacuum metrics in general relativity
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Physicists, mathematicians, and students of general relativity seeking a deeper understanding of gravitational collapse models and their mathematical frameworks.

PeterDonis
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In a previous article, I described in general terms the model of gravitational collapse of a spherically symmetric massive object, first published by Oppenheimer and Snyder in their classic 1939 paper. In this follow-up article, I will give further mathematical details about the model, using an approach somewhat different from their original paper (and inspired by the approach described in MTW and Landau & Lifschitz).
(Note: Weinberg takes a different approach in the vacuum region outside the collapsing matter. Instead of finding an expression for the exterior vacuum metric in comoving coordinates, he finds an expression for the interior metric in coordinates similar to standard Schwarzschild coordinates. We will not discuss that approach here, but it is instructive to compare the two. The latter approach, which also has similarities to the approach taken in the...

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