Maximal hypersurfaces in Robertson-Walker spacetimes

TL;DR

This paper investigates maximal hypersurfaces in specific Robertson-Walker spacetimes, establishing new uniqueness and non-existence results under certain geometric and physical conditions, with applications to notable cosmological models.

Contribution

It introduces new mathematical results on maximal hypersurfaces in open Robertson-Walker spacetimes with Ricci-flat fibers, extending understanding in geometric analysis and cosmology.

Findings

Proves uniqueness of maximal hypersurfaces under certain conditions.

Establishes non-existence of complete maximal hypersurfaces in some spacetimes.

Applies results to models like steady state, Einstein-de Sitter, and radiation universes.

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.