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

Understand

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.