We study stationary black holes in the presence of an external strong magnetic field. In the case where the gravitational backreaction of the magnetic field is taken into account, such an scenario is well described by the Ernst-Wild solution to Einstein-Maxwell field equations, representing a charged, stationary black hole immersed in a Melvin magnetic universe. This solution, however, describes a physical situation only in the region close to the black hole. This is due to the following two reasons: Firstly, Melvin spacetime is not asymptotically locally flat; secondly, the non-static Ernst-Wild solution is not even asymptotically Melvin due to the infinite extension of its ergoregion. All this might seem to be an obstruction to address an scenario like this; for instance, it seems to be an obstruction to compute conserved charges as this usually requires a clear notion of asymptotia. Here, we circumvent this obstruction by providing a method to compute the conserved charges of such a black hole by restricting the analysis to the near horizon region. We compute the Wald entropy, the mass, the electric charge, and the angular momentum of stationary black holes in highly magnetized environments from the horizon perspective, finding results in complete agreement with other formalisms.
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