Second-order phase transitions in black-hole thermodynamics

The physical meaning of second-order phase transitions discovered by Davies (1977) in black-hole thermodynamics is discussed. It is argued that the phenomenon has nothing to do with phase transitions occurring in rotating self-gravitating fluids in Newtonian theory. The authors show that the internal state of a black hole remains unaffected after the phase transition. They also argue that the change of sign and infinite discontinuity in the heat capacity are of purely geometric origin, i.e. are determined by the embedding of an event horizon into a black-hole space-time. This result supports the view that temperature cannot be used as a well-behaved fundamental parameter in black-hole physics.