Extended phase space thermodynamics for third-order Lovelock black holes in diverse dimensions

Abstract

Treating the cosmological constant as thermodynamic pressure and its conjugate as thermodynamic volume, we investigate the critical behavior of the third-order Lovelock black holes in diverse dimensions. For black hole horizons with different normalized sectional curvature $$k=0,\pm 1$$ , the corresponding critical behaviors differ drastically. For $$k=0$$ , there is no critical point in the extended thermodynamic phase space. For $$k=-1$$ , there is a single critical point in any dimension $$d\ge 7$$ , and for $$k=+1$$ , there is a single critical point in $$7$$ dimensions and two critical points in 8, 9, 10, 11 dimensions. We studied the corresponding phase structures in all possible cases.