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We consider the restoration of a spontaneously broken symmetry of aninteracting quantum scalar field around neutral, i.e., Schwarzschild, andelectrically charged, i.e., Reissner-Nordstr\"om, black holes in fourdimensions. This is done through a semiclassical self-consistent procedure, bysolving the system of non-linear coupled equations describing the dynamics ofthe background field and the vacuum polarization. The black hole at its ownhorizon generates an indefinitely high temperature which decreases to theHawking temperature at infinity. Due to the high temperature in its vicinity,there forms a bubble around the black hole in which the scalar field can onlyassume a value equal to zero, a minimum of energy. Thus, in this region thesymmetry of the energy and the field is preserved. At the bubble radius, thereis a phase transition in the value of the scalar field due to a spontaneoussymmetry breaking mechanism. Indeed, outside the bubble radius the temperatureis low enough such that the scalar field settles with a nonzero value in a newenergy minimum, indicating a breaking of the symmetry in this outer region.Conversely, there is symmetry restoration from the outer region to the innerbubble close to the horizon. Specific properties that emerge from differentblack hole electric charges are also noteworthy. It is found that colder blackholes, i.e., more charged ones, have a smaller bubble length of restoredsymmetry. In the extremal case the bubble has zero length, i.e., there is nobubble. Additionally, for colder black holes, it becomes harder to excite thequantum field modes, so the vacuum polarization has smaller values. In theextremal case, the black hole temperature is zero and the vacuum polarizationis never excited.

Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes