Black Hole Formation from a Complete Past for the Einstein–Vlasov System

  • Håkan AndréassonEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 157)


A natural 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 \({\mathring{m}}={\mathring{m}}(r)\) 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 \(t\in (-\infty ,\infty )\). In the present article we review the results in [1].


Black Hole Initial Data Scalar Field Global Existence Vlasov Equation 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Gothenburg and Chalmers University of TechnologyGöteborgSweden

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