Positive mass theorems for asymptotically de Sitter spacetimes

TL;DR

This paper establishes positive mass theorems for asymptotically de Sitter spacetimes by defining conserved quantities at two types of spatial infinities and proving positivity under curvature bounds.

Contribution

It introduces new definitions of total energy, momentum, and angular momentum at different infinities and proves their positivity for specific spacelike hypersurfaces.

Findings

Positive mass theorems for asymptotically de Sitter spacetimes.

Definitions of conserved quantities at two types of spatial infinities.

Positivity results under mean curvature bounds.

Abstract

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to either half of the de Sitter spacetime, we are able to provide definitions of the total energy, the total linear momentum, the total angular momentum, respectively. And we prove two positive mass theorems, corresponding to these two sorts of spatial infinities, for spacelike hypersurfaces whose mean curvatures are bounded by certain constant from above.