  We find hairy black holes of Einstein-Maxwell theory with a complex scalar
field that is confined inside a box in a Minkowski background. These regular
hairy black holes are asymptotically flat and thus the presence of the box or
mirror allows to evade well-known no-hair theorems. We also find the Israel
surface stress tensor that the confining box must have to obey the energy
conditions. In the zero horizon radius limit, these hairy black holes reduce to
a regular asymptotically flat hairy soliton. We find our solutions using
perturbation theory. At leading order, a hairy black hole can be seen as a
Reissner-Nordstrom black hole placed on top of a hairy soliton with the same
chemical potential (so that the system is in thermodynamic equilibrium). The
hairy black holes merge with the Reissner-Nordstrom black hole family at the
onset of the superradiant instability. When they co-exist, for a given energy
and electric charge, hairy black holes have higher entropy than caged
Reissner-Nordstrom black holes. Therefore, our hairy black holes are the
natural candidates for the endpoint of charged superradiance in the
Reissner-Nordstrom black hole mirror system.
