Phase transition for black holes with scalar hair and topological black holes. (English) Zbl 1328.83105
Summary: 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 a black hole with scalar hair (a Martinez-Troncoso-Zanelli black hole) and a 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 the scalar black hole to a non-rotating BTZ black hole.
MSC:
| 83C57 | Black holes |
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