Closed Trapped Surfaces in Cosmology

TL;DR

This paper demonstrates that the presence of closed trapped surfaces in cosmology does not necessarily lead to singularities, especially in spacetimes with compact spatial hypersurfaces, challenging traditional assumptions.

Contribution

It provides examples, including de Sitter spacetime, showing that closed trapped surfaces can exist without implying a cosmological singularity.

Findings

de Sitter spacetime admits many closed trapped surfaces

Closed trapped surfaces do not always indicate singularities

Compact spatial hypersurfaces can avoid singularities despite trapped surfaces

Abstract

The existence of closed trapped surfaces need not imply a cosmological singularity when the spatial hypersurfaces are compact. This is illustrated by a variety of examples, in particular de Sitter spacetime admits many closed trapped surfaces and obeys the null convergence condition but is non-singular in the k=+1 frame.