Stability of MOTS in totally geodesic null horizons

TL;DR

This paper derives the stability operator for MOTS on totally geodesic null horizons, analyzing its properties in non-evolving horizons and applying results to area-angular momentum inequalities in four-dimensional spacetimes.

Contribution

It provides the explicit form of the stability operator for MOTS on totally geodesic null horizons and explores its implications for horizon stability and geometric inequalities.

Findings

Explicit stability operator derived for MOTS on null horizons

Stability properties linked to surface gravity and minimal sections

Established area-angular momentum inequality for axially symmetric horizons

Abstract

Closed sections of totally geodesic null hypersurfaces are marginally outer trapped surfaces (MOTS), for which a well-defined notion of stability exists. In this paper we obtain the explicit form for the stability operator for such MOTS and analyze in detail its properties in the particular case of non-evolving horizons, which include both isolated and Killing horizons. We link these stability properties with the surface gravity of the horizon and/or to the existence of minimal sections. The results are used, in particular, to obtain an area-angular momentum inequality for sections of axially symmetric horizons in four spacetime dimensions, which helps clarifying the relationship between two different approaches to this inequality existing in the literature.