Phase transitions in charged topological black holes dressed with a scalar hair

Understand

Phase transitions in charged topological black holes dressed with a scalar field are studied.

• These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field.
• Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found.
• The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant.