New approach to phase transitions in black holes

We develop an analogy between fluids and black holes to study phase transitions in the latter. The entropy-temperature graph shows the onset of a phase transition without any latent heat. The nature of this continuous (higher order) phase transition is examined in details. We find that the second order derivatives of the free energy diverge at the critical temperature. Also, the transition is smeared instead of sharp, so that the usual Ehrenfest's scheme breaks down. A generalised version of this scheme is formulated which is shown to be consistent with the phase transition curves.