  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.
