New type of phase transition in Reissner Nordstr\"om - AdS black hole and its thermodynamic geometry

TL;DR

This paper investigates the phase transition behavior of Reissner-Nordström-AdS black holes, revealing a novel glassy-type transition and analyzing thermodynamic geometry to identify critical points.

Contribution

It introduces a new type of phase transition in RN-AdS black holes, characterized by deviations from Ehrenfest's equations and thermodynamic geometric analysis.

Findings

No first order phase transition due to continuous entropy.

Second Ehrenfest's equation is violated, ruling out second order transition.

Scalar curvature diverges at heat capacity divergence points.

Abstract

The phase transition of a RN-AdS black hole is studied in details using Ehrenfest's equations. There is no discontinuity in entropy which signals a lack of any first order phase transition. We then show that although Ehrenfest's first equation is satisfied, the second is not, so that a true second order phase transition is also ruled out. However this deviation from the second Ehrenfest's equation, for a certain range of the black hole charge, indicates the existence of a new glassy type transition. We finally study the thermodynamic behaviour using state space geometry and find that the scalar curvature diverges exactly at those points where the heat capacity diverges.