Abstract
A classical question in general relativity is classifying regular static black hole solutions of the static Einstein–Maxwell equations (or electrovacuum system). We prove some classification results for an electrovacuum system such that the electric potential is a smooth function of the lapse function. We particularly show that an n-dimensional locally conformally flat electrovacuum space satisfying (1.8) must be in the Majumdar–Papapetrou class. Moreover, we prove that an n-dimensional electrovacuum space satisfying (1.7) with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product manifold with \((n-1)\)-dimensional Einstein fibers. Finally, a three-dimensional electrovacuum space satisfying (1.7) with a third-order divergence-free Cotton tensor is also classified.
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Communicated by Mihalis Dafermos.
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Benedito Leandro was partially supported by CNPq/Brazil Grant 303157/2022-4. Róbson Lousa was supported by PROPG-CAPES [Finance Code 001]. The authors were partially supported by CNPq/Brazil Grant 403349/2021-4.
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Leandro, B., Andrade, M. & Lousa, R. On the Geometry of Electrovacuum Spaces in Higher Dimensions. Ann. Henri Poincaré 24, 3153–3184 (2023). https://doi.org/10.1007/s00023-023-01306-0
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DOI: https://doi.org/10.1007/s00023-023-01306-0