Maxwell’s equal-area law for Gauss–Bonnet–Anti-de Sitter black holes

Interpreting the cosmological constant Λ as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we study the Maxwell equal-area law of higher dimensional Gauss–Bonnet–AdS black holes in extended phase space. These black hole solutions critically behave like van der Waals systems. It has been realized that below the critical temperature Tc the stable equilibrium is violated. We show through calculations that the critical behaviors for the uncharged black holes only appear in $$d=5$$ . For the charged case, we analyze solutions in $$d = 5$$ and $$ d = 6$$ separately and find that, up to some constraints, the critical behaviors only appear in the spherical topology. Using the Maxwell construction, we also find the isobar line for which the liquid–gas-like phases coexist.