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A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system

We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.

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1. Mathematisches Institut der Universität München, Theresienstr. 39, D-80333, München, Germany

   Gerhard Rein

2. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85740, Garching bei München, Germany

   Alan D. Rendall

3. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

   Jack Schaeffer

1. Gerhard Rein
2. Alan D. Rendall
3. Jack Schaeffer

Communicated by S. T. Yau

Research supported in part by NSF DMS 9101517

Rein, G., Rendall, A.D. & Schaeffer, J. A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system. Commun.Math. Phys. 168, 467–478 (1995). https://doi.org/10.1007/BF02101839

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• Received: 23 June 1993

• Issue Date: April 1995

• DOI: https://doi.org/10.1007/BF02101839

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