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

TL;DR

This paper explores the thermodynamic phase behavior of third order Lovelock black holes across various dimensions by treating the cosmological constant as pressure, revealing diverse critical phenomena depending on horizon curvature and dimension.

Contribution

It provides a comprehensive analysis of phase transitions for Lovelock black holes in different dimensions and curvature cases within the extended thermodynamic framework.

Findings

No critical point for flat horizons ($k=0$).

Single critical point for hyperbolic horizons ($k=-1$) in dimensions ≥7.

Multiple critical points for spherical horizons ($k=+1$) in higher 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 $k=0,\pm1$, 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 $d\geq 7$, and for $k=+1$, there is a single critical point in $7$ dimension and two critical points in $8,9,10,11$ dimensions. We studied the corresponding phase structures in all possible cases.