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The global nonlinear stability of Minkowski space for the massless Einstein-Vlasov system. (English) Zbl 06919598
Summary: Minkowski space is shown to be globally stable as a solution to the Einstein-Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the “wave zone”, and then proving a small data semi-global existence result for the characteristic initial value problem for the massless Einstein-Vlasov system in this region. This relies on weighted estimates for the solution which, for the Vlasov part, are obtained by introducing the Sasaki metric on the mass shell and estimating Jacobi fields with respect to this metric by geometric quantities on the spacetime. The stability of Minkowski space result for the vacuum Einstein equations is then appealed to for the remaining regions.

35Q83 Vlasov equations
35Q76 Einstein equations
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
35B35 Stability in context of PDEs
Full Text: DOI
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