Renato Velozo (University of Cambridge): Stability of Schwarzschild for the spherically symmetric Einstein--massless Vlasov system. Oberseminar Topics in General Relativity
Tuesday, 24.05.2022 12:00 im Raum SRZ204
The Einstein--massless Vlasov system is a relevant model in the study of collisionless many particle systems in general relativity. In this talk, I will present a stability result for the exterior of Schwarzschild as a solution of this system assuming spherical symmetry. We exploit the hyperbolicity of the geodesic flow around the black hole to obtain decay of the stress energy momentum tensor, despite the presence of trapped null geodesics. The main result requires a precise understanding of radial derivatives of the energy momentum tensor, which we estimate using Jacobi fields on the tangent bundle in terms of the Sasaki metric.