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

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.

This is a pre-print of an article published in General Relativity and Gravitation. The final authenticated version is available online at: https://doi.org/10.1007/s10714-016-2183-6

References in corpus (3)

• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Spacelike hypersurfaces with constant mean curvature in the steady state space

Cited by in corpus (2)

• Constant mean curvature spacelike hypersurfaces in spatially open GRW spacetimes
• Extremal and weakly trapped submanifolds in Generalized Robertson-Walker spacetimes