Mathematische Annalen

, Volume 350, Issue 3, pp 683–705 | Cite as

The formation of black holes in spherically symmetric gravitational collapse

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Abstract

We consider the spherically symmetric, asymptotically flat Einstein–Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines \({r=c\in [0,2M]}\) are incomplete, and for r > 2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We give examples of such initial data with the additional property that the solutions exist for all r ≥ 0 and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.

Keywords

Black Hole Gravitational Collapse Vlasov Equation Outer Domain Cosmic Censorship 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Håkan Andréasson
    • 1
  • Markus Kunze
    • 2
  • Gerhard Rein
    • 3
  1. 1.Mathematical Sciences, Chalmers University of TechnologyGöteborg UniversityGöteborgSweden
  2. 2.Fachbereich MathematikUniversität Duisburg-EssenEssenGermany
  3. 3.Mathematisches Institut der Universität BayreuthBayreuthGermany

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