Initial data rigidity results

TL;DR

This paper establishes new rigidity results for initial data sets in general relativity, focusing on conditions that guarantee certain geometric properties, with implications for the positive mass theorem.

Contribution

It introduces novel rigidity conditions for initial data sets and extends known results to cases involving marginally outer trapped surfaces and scalar curvature bounds.

Findings

Conditions ensuring a marginally outer trapped surface is 'weakly outermost'

Rigidity results for Riemannian manifolds with scalar curvature bounds

Connections to the positive mass theorem

Abstract

We present several rigidity results for initial data sets motivated by the positive mass theorem. An important step in our proofs here is to establish conditions that ensure that a marginally outer trapped surface is "weakly outermost". A rigidity result for Riemannian manifolds with a lower bound on their scalar curvature is included as a special case.