Black holes in magnetic universes

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