Existence of Static Solutions to the Vlasov-Poisson and Einstein-Vlasov Systems as Fixed Points of a Mass-Preserving Algorithm

Abstract

This thesis develops a new method for proving the existence of static, spherically symmetric solutions to the Einstein–Vlasov system by reformulating a masspreserving algorithm as a fixed-point problem. Building on earlier work for the Vlasov–Poisson system, we first extend an existing fixed-point existence proof from isotropic to anisotropic solutions. We then establish the corresponding result for the Einstein–Vlasov system, using a simple isotropic ansatz.