Paper in proceedings, 2014

Anatural question in general relativity is to find initial data for the Einstein equations whose past evolution is regular and whose future evolution contains a black hole. In [1] initial data of this kind is constructed for the spherically symmetric Einstein–Vlasov system. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass (Formula presented) (r) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is analogous to the result [2] 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 the present article we review the results in [1].

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

1867-4941 (eISSN)

Vol. 157 11-18Computational Mathematics

10.1007/978-3-319-06761-2_2

978-3-319-06760-5