Rigidity of outermost MOTS - the initial data version

TL;DR

This paper presents a new initial data approach to the rigidity of outermost MOTS, simplifying previous proofs and advancing understanding of black hole topology without bending the initial data manifold.

Contribution

It provides a pure initial data version of the rigidity result for outermost MOTS, removing the need for bending the initial data manifold in the proof.

Findings

Pure initial data rigidity result for outermost MOTS

Implication for black hole topology in higher dimensions

Simplified proof avoiding bending of initial data manifold

Abstract

In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes [8]. The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.