A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold

摘要

We revisit and generalize a recent result of Cederbaum (Cederbaum in preparation; Cederbaum 2017 Oberwolfach Report) concerning the rigidity of the Schwarzschild manifold for spin manifolds. This includes the classical black hole uniqueness theorems (Bunting and Masood-ul-Alam 1987 Gen. Relativ. Gravit. 19 147; Gibbons, Ida and Shiromizu 2002 Phys. Rev. Lett. 89 041101; Hwang 1998 Geom. Dedicata 71 5) as well as the more recent uniqueness theorems for photon spheres (Cederbaum 2015 Contemp. Math. 667 86; Cederbaum and Galloway 2017 Commun. Anal. Geom. 25 303; Cederbaum and Fehrenbach personal communication).