Short-time existence of Ricci flow in standard static spacetimes

Abstract

We prove the short-time existence of Ricci flow in the class of standard static spacetimes with a closed and compact Riemannian spatial component. The proof constitutes establishing parabolicity of the Ricci-DeTurck flow system which therefore, by existence and uniqueness theorem, admits a short-time solution. Finally pulling this solution back via an appropriate family of diffeomorphisms yields a solution to the original Ricci flow.