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arXiv · 2410.06701

Oppenheimer-Snyder type collapse for a collisionless gas

Håkan Andréasson·Gerhard Rein
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Abstract

In 1939, Oppenheimer and Snyder showed that the continued gravitational collapse of a self-gravitating matter distribution can result in the formation of a black hole, cf.~ \cite{OS}. In this paper, which has greatly influenced the evolution of ideas around the concept of a black hole, matter was modeled as dust, a fluid with pressure equal to zero. We prove that when the corresponding initial data are suitably approximated by data for a collisionless gas as modeled by the Vlasov equation, then a trapped surface forms before the corresponding solution to the Einstein-Vlasov system can develop a singularity and again a black hole arises. As opposed to the dust case the pressure does not vanish for such solutions. As a necessary starting point for the analysis, which is carried out in Painlev\'{e}-Gullstrand coordinates, we prove a local existence and uniqueness theorem for regular solutions together with a corresponding extension criterion. The latter result will also become useful when one perturbs dust solutions containing naked singularities in the Vlasov framework.

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Håkan Andréasson, Gerhard Rein. 2024-10-09. Oppenheimer-Snyder type collapse for a collisionless gas. https://arxiv.org/abs/2410.06701

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