Quasi-Round MOTSs and Stability of the Schwarzschild Null Penrose Inequality

TL;DR

This paper investigates the geometry and stability of quasi-round MOTSs within null hypersurfaces, establishing conditions under which the Null Penrose Inequality holds in perturbed Schwarzschild spacetimes.

Contribution

It introduces the concept of quasi-round MOTSs, proves their existence and stability under perturbations, and identifies conditions ensuring the Null Penrose Inequality in Schwarzschild spacetime.

Findings

Existence of a unique foliation by quasi-round MOTS for certain horizons

Persistence of quasi-round MOTS under spacetime perturbations

Conditions on null hypersurface asymptotics that imply the Null Penrose Inequality

Abstract

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, for a class of strictly stable Weakly Isolated Horizons, we show the existence of a unique foliation by quasi-round MOTS. In the second part, we show that any subsequent space-time perturbation continues to admit a quasi-round MOTS. Finally, for perturbations of the quasi-round MOTS in Schwarzschild, we identify sufficient conditions on the asymptotics of any past-pointing null hypersurface that yields the Null Penrose Inequality.