Foliation of null cones by surfaces of constant spacetime mean curvature near MOTS

TL;DR

This paper demonstrates that near a stable MOTS in a null cone, one can foliate the region with hypersurfaces of constant spacetime mean curvature, providing new methods for constructing such surfaces.

Contribution

It introduces flow techniques to foliate neighborhoods of stable MOTS with constant spacetime mean curvature surfaces and offers methods to construct prescribed curvature surfaces.

Findings

Neighborhood of stable MOTS can be foliated by constant spacetime mean curvature surfaces

Flow techniques are effective for constructing these hypersurfaces

Provides methods for constructing prescribed curvature surfaces within null cones

Abstract

Marginally Outer Trapped Surfaces (MOTS) in spacetimes are well-known to indicate the existence of black holes. Using flow techniques, we prove that a neighbourhood of a stable MOTS in a null cone may be foliated by hypersurfaces of constant spacetime mean curvature. We also provide methods to construct prescribed spacetime mean curvature surfaces within null cones.