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

Understand

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.