Phase transition between non-extremal and extremal Reissner-Nordstr\"om black holes

TL;DR

This paper investigates the phase transition between non-extremal and extremal Reissner-Nordström black holes, highlighting the conditions under which such transitions occur or are forbidden, and analyzing related thermodynamic processes.

Contribution

It provides a detailed analysis of the phase transition at zero temperature limit and the thermodynamic constraints preventing reverse transitions in Reissner-Nordström black holes.

Findings

Evaporation from non-extremal to extremal black holes is possible.

Reverse transition from extremal to non-extremal black holes is forbidden due to maximum temperature.

Hawking-Page transition is unlikely in AdS Reissner-Nordström black holes.

Abstract

We discuss the phase transition between non-extremal and extremal Reissner-Nordstr\"om black holes. This transition is considered as the $T \to 0$ limit of the transition between the non-extremal and near-extremal black holes. We show that an evaporating process from non-extremal black hole to extremal one is possible to occur, but its reverse process is not possible to occur because of the presence of the maximum temperature. Furthermore, it is shown that the Hawking-Page phase transition between small and large black holes unlikely occurs in the AdS Reissner-Nordstr\"om black holes.