Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-01-17
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages. Revised version to appear in Annales Henri Poincar\'e
Scientific paper
Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a "realistic" matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass $\open{m}=\open{m}(r)$ and the area radius $r$ is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is in a sense analogous to the result for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time $t\in (-\infty,\infty)$.
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