Horizon area bound and MOTS stability in locally rotationally symmetric solutions

TL;DR

This paper investigates the stability and area bounds of marginally outer trapped surfaces (MOTS) in locally rotationally symmetric perfect fluid spacetimes, revealing conditions for stability, topology constraints, and non-existence results.

Contribution

It provides new bounds on MOTS area, characterizes stability conditions, and explores topological and non-existence aspects in LRS spacetimes, including imperfect fluids.

Findings

Upper bound on stable MOTS area

Stable MOTS must be strictly outermost

Non-existence results for certain configurations

Abstract

In this paper, we study the stability of marginally outer trapped surfaces (MOTS), foliating horizons of the form $r=X(\tau)$, embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ``outside" of and homologous to $\mathcal{S}$. Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ``growth" of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.