A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold. (22nd March 2021)

• Record Type: Journal Article
• Authors: Raulot, Simon
• Is Part Of: Classical and quantum gravity. Volume 38:Number 8(2021)
• Publication Date: 2021-03-22
• Subjects: Einstein field equations -- Schwarzschild spacetime -- rigidity -- spinors -- Dirac operator; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/abe4ec
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: 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).