New approach to phase transitions in black holes

TL;DR

This paper explores phase transitions in black holes by drawing analogies with fluid systems, revealing a continuous transition characterized by diverging derivatives and a smeared nature, challenging traditional thermodynamic schemes.

Contribution

It introduces a novel analogy between fluids and black holes to analyze phase transitions, and develops a generalized Ehrenfest scheme for continuous transitions in black hole thermodynamics.

Findings

Second derivatives of free energy diverge at critical temperature

Phase transition occurs without latent heat

Transition is smeared, breaking traditional Ehrenfest scheme

Abstract

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.