Maximal hypersurfaces in Robertson-Walker spacetimes

Abstract

In this work we study maximal hypersurfaces in spatially open Generalized Robertson-Walker spacetimes with Ricci-flat fiber by means of a generalized maximum principle. In particular, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-Walker spacetimes with flat fiber. Moreover, our results are applied to relevant spacetimes as the steady state spacetime, Einstein-de Sitter spacetime and radiation models.