A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold

TL;DR

This paper provides a spinorial proof demonstrating the rigidity of the Riemannian Schwarzschild manifold, extending classical and recent black hole uniqueness theorems within a unified framework.

Contribution

It introduces a novel spinorial approach to prove the rigidity of the Schwarzschild manifold, generalizing previous results and encompassing various black hole uniqueness theorems.

Findings

Spinorial proof confirms Schwarzschild rigidity

Unifies classical and recent black hole theorems

Extends rigidity results to broader contexts

Abstract

We revisit and generalize a recent result of Cederbaum [C2, C3] concerning the rigidity of the Schwarzschild manifold for spin manifolds. This includes the classical black hole uniqueness theorems [BM, GIS, Hw] as well as the more recent uniqueness theorems for pho-ton spheres [C1, CG1, CG2].