Phase transition for black holes with scalar hair and topological black holes

Understand

We study phase transitions between black holes with scalar hair and topological black holes in asymptotically anti-de Sitter spacetimes.

• As the ground state solutions, we introduce the non-rotating BTZ black hole in three dimensions and topological black hole with hyperbolic horizon in four dimensions.
• For the temperature matching only, we show that the phase transition between black hole with scalar hair (Martinez-Troncoso-Zanelli black hole) and topological black hole is second-order by using differences between two free energies.
• However, we do not identify what order of the phase transition between scalar and non-rotating BTZ black holes occurs in three dimensions, although there exists a possible decay of scalar black hole to non-rotating BTZ black hole.