Vacuum energy and the latent heat of AdS-Kerr black holes

Phase transitions for rotating asymptotically anti-de Sitter black holes in four dimensions are described in the P - T plane, in terms of the Hawking temperature and the pressure provided by the cosmological constant. The difference between constant angular momentum and constant angular velocity is highlighted; the former has a second order phase transition while the latter does not. If the angular momentum is fixed there a line of first order phase transitions terminating at a critical point with a second order phase transition and vanishing latent heat, while if the angular velocity is fixed there is a line of first order phase transitions terminating at a critical point with infinite latent heat. For constant angular velocity the analytic form of the phase boundary is determined, latent heats derived and the Clapeyron equation verified.