Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: Håkan Andréasson, Markus Kunze and Gerhard Rein
Journal: Quart. Appl. Math. 68 (2010), 17-42
MSC (2000): Primary 35Q75; Secondary 83C75, 85A05
DOI: https://doi.org/10.1090/S0033-569X-09-01165-9
Published electronically: October 15, 2009
MathSciNet review: 2598878
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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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Additional Information

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

DOI: https://doi.org/10.1090/S0033-569X-09-01165-9
Keywords: General relativity, Einstein-Vlasov system, gravitational collapse, black holes
Received by editor(s): December 9, 2008
Published electronically: 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
Article copyright: © Copyright 2009 Brown University


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