The formation of black holes in spherically symmetric gravitational collapse

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 also give examples of such initial data with the additional property that the solutions exist for all $r\ge 0$ 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.

36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modifications

References in corpus (5)

• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• On the steady states of the spherically symmetric Einstein-Vlasov system
• On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
• Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

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