# On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson Walker spacetime

## TL;DR

This paper characterizes the foliation by spacelike slices in generalized Robertson-Walker spacetimes using a mean curvature equation, providing a complete classification under natural assumptions, especially in de Sitter spacetime.

## Contribution

It offers a new characterization of spacelike foliations in GRW spacetimes via a mean curvature equation and solves the case in de Sitter spacetime using a novel integral formula application.

## Key findings

- All entire solutions of the mean curvature equation are classified under certain assumptions.
- The case of spacelike graphs in de Sitter spacetime is fully solved.
- A new application of an integral formula is used to achieve the classification.

## Abstract

A characterization of the foliation by spacelike slices of an $(n+1)$-dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some natural assumptions, of physical or geometric nature, all the entire solutions of such an equation are obtained. In particular, the case of entire spacelike graphs in de Sitter spacetime is faced and completely solved by means of a new application of a known integral formula.