  When approaching extremality, rotating black holes tend to expel the magnetic
field in which they are immersed. This phenomenon, being reminiscent of the
Meissner-Ochsenfeld effect in superconductors, is known as the black hole
Meissner effect, and here we study it in the backreacting regime and from the
near horizon perspective. By resorting to methods recently developed in the
literature, which allow to compute conserved charges in the near horizon
region, regardless the details of the asymptotia at large distance, we
investigate the properties of the black hole horizon when in its Meissner
state. We show that, when in such state, the horizon exhibits two sets of
supertranslation symmetries as well as a symmetry generated by the local
conformal group. The supertranslations are generated by two infinite sets of
currents, one of which comes from local dilations of the advanced null
coordinate at the horizon, and the other from local gauge transformations that
preserve the electromagnetic field configuration at the horizon. We show that
the evaluation of the conserved charges associated to these symmetries
correctly reproduce the physical charges of the magnetized black holes and
their thermodynamics. This represents a concrete application of the techniques
developed in [1,2,3] and it extends the results of [4] to arbitrary values of
the black hole charges. In addition, we elaborate on the charges computation at
the horizon: we show the equivalence between the horizon charges and the
evaluation of the corresponding Komar integrals. Besides, we show the validity
of the Gauss phenomenon by explicitly relating near horizon charges with fluxes
and charges computed by other techniques. All this provides a method to derive
the thermodynamics of magnetized horizons in a quite succinct way, including
the case of horizons exhibiting the Meissner effect.
