Spacelike hypersurfaces with negative total energy in de Sitter spacetime

TL;DR

This paper constructs spacelike hypersurfaces with negative total energy in half-de Sitter spacetimes, extending previous positive energy theorems to cases where mean curvature bounds are violated.

Contribution

It introduces new examples of hypersurfaces with negative total energy in half-de Sitter spacetimes, beyond the previously studied asymptotic conditions.

Findings

Existence of spacelike hypersurfaces with negative total energy.

Extension of positive energy theorems to cases with unbounded mean curvature.

Construction of hypersurfaces violating earlier curvature bounds.

Abstract

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $\P$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial data sets by the second author and collaborators. These initial data sets are asymptotic to time slices of the two kinds of half-de Sitter spacetimes respectively, and their mean curvatures are bounded from above by certain constants. While the mean curvatures violate these conditions, the spacelike hypersurfaces with negative total energy in the two kinds of half-de Sitter spacetimes are constructed in this short paper.