Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes |
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Authors: | Alberto A. Garcí a, |
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Affiliation: | aDepartamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apdo. Postal 14-740, 07000 México, DF, Mexico;bDepartment of Physics, University of California, Davis, CA 95616, USA |
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Abstract: | From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants FμνFμν and TμνTμν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention. |
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Keywords: | Exact solutions Anti-de Sitter 2  +  1 gravity Electromagnetism Black holes |
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