Constant mean curvature spacelike hypersurfaces in spatially open GRW spacetimes
Jos\'e A. S. Pelegr\'in, Marco Rigoli
TL;DR
This paper establishes new uniqueness and non-existence results for complete spacelike hypersurfaces with constant mean curvature in open GRW spacetimes, with applications to specific cosmological models.
Contribution
It provides novel geometric and physical conditions under which such hypersurfaces are unique or do not exist in certain cosmological spacetimes.
Findings
New uniqueness results for spacelike hypersurfaces in open GRW spacetimes
Non-existence results under specific geometric assumptions
Applications to steady state, Einstein-de Sitter, and radiation spacetimes
Abstract
In this paper we provide under certain geometric and physical assumptions new uniqueness and non-existence results for complete spacelike hypersurfaces of constant mean curvature in spatially open Generalized Robertson-Walker spacetimes. Some of our results are then applied to relevant spacetimes as the steady state spacetime, Einstein-de Sitter spacetime and certain radiation models.
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