A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold

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].

References in corpus (2)

• Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes
• A Positive Mass Theorem for Manifolds with Boundary

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• Uniqueness of equipotential photon surfaces in 4-dimensional static vacuum asymptotically flat spacetimes for positive, negative, and zero mass -- and a new partial proof of the Willmore inequality
• First boundary Dirac eigenvalue and boundary capacity potential