On black holes in magnetic universes

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Abstract
The magnetized black hole solutions discovered by Ernst are studied. It is shown that no static magnetic‐universe Kerr–Newman black holes exist if either a, the Kerr angular momentum parameter, or e, the electric charge parameter, is nonzero. Robinson’s identity is used to prove that the Schwarzschild–Melvin black hole solution is the unique static, axisymmetric black hole solution of the sourceless Einstein–Maxwell equations which asymptotically resembles Melvin’s magnetic universe. This may be viewed as a generalization of Israel’s theorem, in which one extra assumption (axisymmetry) is required, but the boundary conditions at infinity are somewhat relaxed.

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