Article

The formation of black holes in spherically symmetric gravitational collapse

Mathematische Annalen (impact factor: 1.3). 04/2012; 350(3):683-705. DOI:10.1007/s00208-010-0578-3 pp.683-705
Source: arXiv

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 Î [0,2M]{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.

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Keywords

asymptotically flat Einstein–Vlasov system

black hole

Einstein equations

examples

following properties

general matter model

geodesic

global existence

initial data

mass M

metric converges asymptotically

resulting spacetime

Schwarzschild metric

spherically symmetric