Rigidity of outermost MOTS - the initial data version

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.

8 pages; v2: minor changes; version to appear in GRG

References in corpus (1)

• Rigidity of marginally outer trapped 2-spheres

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• Marginally Outer Trapped Tori in Black Hole Spacetimes
• Topology of Cosmological Black Holes
• Rigidity aspects of Penrose's singularity theorem
• On the genericity of singularities in spacetimes with weakly trapped submanifolds