Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
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arXiv
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| Format: | Preprint |
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2024
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| author | Borghini, Stefano Cederbaum, Carla Cogo, Albachiara |
| author_facet | Borghini, Stefano Cederbaum, Carla Cogo, Albachiara |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes Borghini, Stefano Cederbaum, Carla Cogo, Albachiara General Relativity and Quantum Cosmology Differential Geometry 53Z05, 35Q75, 83C57 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. |
| title | Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes |
| topic | General Relativity and Quantum Cosmology Differential Geometry 53Z05, 35Q75, 83C57 |
| url | https://arxiv.org/abs/2401.05253 |