A note on Maxwell's equal area law for black hole phase transition

Understand

The state equation of the charged AdS black hole is reviewed in the $T-r$ plane.

• Thinking of the phase transition, the $T-S$, $P-V$, $P-\nu$ graphs are plotted and then the equal area law is used in the three cases to get the phase transition point (P,T).
• The analytical phase transition point relations for P-T of charged AdS black hole has been obtained successfully.
• By comparing the three results, we find that the equal area law possibly cannot be used directly for $P-\nu$ plane.