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Global existence of solutions of the spherically symmetric Vlasov- Einstein system with small initial data. (English) Zbl 0774.53056
The coupled Einstein-Vlasov system describes a self-gravitating collisionless gas within general relativity. The present paper establishes existence of global spherically symmetric and asymptotically flat solutions to small initial data. The proof consists in the construction of a local solution of the Cauchy problem and in some continuation argument. As one conclusion, cosmic censorship holds for the Einstein-Vlasov system.

MSC:
53Z05 Applications of differential geometry to physics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
58J47 Propagation of singularities; initial value problems on manifolds
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