Quarterly of Applied Mathematics

Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system

Author(s): Håkan Andréasson; Markus Kunze; Gerhard Rein
Journal: Quart. Appl. Math.
MSC (2000): Primary 35Q75; Secondary 83C75, 85A05
Posted: October 15, 2009
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Abstract: We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution. Among these data there are data such that the corresponding solutions exist globally in Schwarzschild coordinates. We put these results into a more general context, and we include arguments which show that the spacetimes we obtain satisfy the weak cosmic censorship conjecture and contain a black hole in the sense of suitable mathematical definitions of these concepts which are available in the literature.

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Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35Q75, 83C75, 85A05

Håkan Andréasson
Affiliation: Mathematical Sciences, Chalmers University of Technology, Göteborg University, S-41296 Göteborg, Sweden
Email: hand@math.chalmers.se

Markus Kunze
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, D-45117 Essen, Germany
Email: markus.kunze@uni-due.de

Gerhard Rein
Affiliation: Mathematisches Institut der Universität Bayreuth, D-95440 Bayreuth, Germany
Email: gerhard.rein@uni-bayreuth.de

PII: S0033-569X-09-01165-9
Keywords: General relativity, Einstein-Vlasov system, gravitational collapse, black holes
Received by editor(s): December 9, 2008
Posted: October 15, 2009
Additional Notes: Support of the first author by the Institut Mittag-Leffler (Djursholm, Sweden) is gratefully acknowledged.
Dedicated: Dedicated to Prof. W. A. Strauss on the occasion of his 70th birthday
Copyright of article: Copyright 2009, Brown University

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