Abstract
AbstractWe study four-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 equipotential 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) equipotential photon surfaces in the super-extremal case, not yet treated in the literature.
Published Version
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