Eur. Phys. J. C (2015) 75: 71
https://doi.org/10.1140/epjc/s10052-015-3299-7

Regular Article - Theoretical Physics

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

¹ Département de Physique, Faculté Polydisciplinaire, Université Sultan Moulay Slimane, Béni Mellal, Morocco
² High Energy Physics and Astrophysics Laboratory, FSSM, Cadi Ayyad University, Marrakesh, Morocco
³ Département de Physique, LHESIR, Faculté des Sciences, Université Ibn Tofail, Kénitra, Morocco
⁴ Ecole Nationale des Sciences Appliquées, Université Mohammed Premier, Ajdir, BP: 3, 32003, Al Hoceima, Morocco

^* e-mail: hasan.elmoumni@edu.uca.ma

Received: 14 December 2014
Accepted: 29 January 2015
Published online: 17 February 2015

Abstract

Interpreting the cosmological constant 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 the stable equilibrium is violated. We show through calculations that the critical behaviors for the uncharged black holes only appear in . For the charged case, we analyze solutions in and 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.