Linear and non-linear stability of collisionless many-particle systems on black hole exteriors.

Abstract: I will present upcoming linear and non-linear stability results concerning the asymptotic behavior of collisionless many-particle systems on black hole exteriors. On the one hand, I will discuss decay properties for solutions to the massive Vlasov equation on Schwarzschild spacetime. On the other hand, I will discuss an asymptotic stability result for the exterior of Schwarzschild as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. I will explain the use of hyperbolic dynamics to obtain decay in time of the energy momentum tensor by considering a Vlasov equation with a trapping potential.

Posted on Apr 6, 2023 in Differential Equations, Seminars