Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes

2024/01/10 by Stefano Borghini, Borghini, Stefano, Carla Cederbaum +3 · 1 citation
Physics and Astronomy · #35Q75 #53Z05 #83C57 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.2401.05253

openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study 4-dimensional asymptotically flat electrostatic electro-vacuum spacetimes with a connected black hole, photon sphere, or equipotential photon surface inner boundary. Our analysis, inspired by the potential theory approach by Agostiniani-Mazzieri, allows to give self-contained proofs of known uniqueness theorems of the sub-extremal, extremal and super-extremal Reissner-Nordström spacetimes. We also obtain new results for connected photon spheres and for connected photon surfaces in the extremal case. Finally, we provide, up to a restriction on the range of their radii, the uniqueness result for connected (both non-degenerate and degenerate) photon surfaces in the super-extremal case, not yet treated in the literature.

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