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- Andreasson, Håkan, 1966, et al.
(författare)
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Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
- 2010
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Ingår i: Journal of Hyperbolic Differential Equations. - Göteborg : Chalmers University of Technology. - 0219-8916. ; 7:4, s. 707-731
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Tidskriftsartikel (refereegranskat)abstract
- We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.
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| 2. |
- Andreasson, Håkan, 1966, et al.
(författare)
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The formation of black holes in spherically symmetric gravitational collapse
- 2011
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Ingår i: MATHEMATISCHE ANNALEN. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 350:3, s. 683-705
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Tidskriftsartikel (refereegranskat)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 [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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