Princeton University Gravity Initiative Seminar

Abstract: We will present a commutation vector field approach for the solutions to the massless Vlasov equation on the exterior of a Schwarzschild spacetime, together with extensions to subextremal Kerr black holes. The approach satisfies two properties. First, it provides decay estimates for the energy flux induced by the energy-momentum tensor of Vlasov fields and its derivatives. Secondly, it is compatible with the methods used to study wave equations on black hole spacetimes.

For this, we make use of a weight function that captures the concentration properties of the geodesic flow. By using a well-chosen modification of its symplectic gradient, we construct a norm for which any smooth solution to the massless Vlasov equation satisfies an integrated energy decay estimate without relative degeneration. This is joint work with Renato Velozo.