Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details

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The discussion elaborates on the Oppenheimer-Snyder model of gravitational collapse, focusing on the mathematical details that extend beyond the original 1939 paper. The author introduces a new approach inspired by MTW and Landau & Lifschitz, differing from Oppenheimer and Snyder's methods. Additionally, it highlights Weinberg's alternative approach in the vacuum region, which contrasts with the interior metric analysis. The comparison between these methodologies is noted as a valuable exercise, although it is not the main focus of the article. The conversation emphasizes the importance of understanding different mathematical frameworks in gravitational collapse.
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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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