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arXiv · 2401.05253

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

Stefano Borghini·Carla Cederbaum·Albachiara Cogo
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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-Nordstr\"om 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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Stefano Borghini, Carla Cederbaum, Albachiara Cogo. 2024-01-10. Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes. https://doi.org/10.1007/s00023-024-01514-2

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