Uniqueness of complete maximal hypersurfaces in spatially open $(n+1)$-dimensional Robertson-Walker spacetimes with flat fiber

TL;DR

This paper establishes new uniqueness and non-existence results for complete maximal hypersurfaces in certain open Robertson-Walker spacetimes with flat fibers, with applications to models like steady state, Einstein-de Sitter, and radiation spacetimes.

Contribution

It provides novel geometric and physical conditions ensuring uniqueness or non-existence of maximal hypersurfaces in these spacetimes.

Findings

Uniqueness results for maximal hypersurfaces under specific conditions.

Non-existence results in certain physically relevant spacetimes.

Applications to steady state, Einstein-de Sitter, and radiation models.

Abstract

In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-Walker spacetimes whose fiber is flat. Moreover, our results are applied to relevant spacetimes as the steady state spacetime, Einstein-de Sitter spacetime and radiation models.