Title: On quantitative gravitational relaxation
Abstract: We obtain quantitative decay rates for the linearised gravitational potential around compactly supported steady states of the Vlasov-Poisson system featuring a point mass potential at the origin. Such steady states feature stably trapped particles which present a severe obstacle to any kind of dispersion. The problem is further complicated by the presence of an infinite-dimensional kernel. To handle these issues we combine tools from dynamical systems, Hamiltonian geometry, and scattering theory. Our theorem can be viewed as a first quantitative proof of (linear) gravitational Landau damping. Joint work with Matthew Schrecker.