P-V criticality in the extended phase space of black holes in massive gravity

Understand

We study the P-V criticality and phase transition in the extended phase space of charged anti-de Sitter black holes in canonical ensemble of ghost-free massive gravity, where the cosmological constant is viewed as a dynamical pressure of the black hole system.

• We give the generalized thermodynamic first law and the Smarr relation with massive gravity correction.
• We find that not only when the horizon topology is spherical but also in the Ricci flat or hyperbolic case, there appear the P-V criticality and phase transition up to the combination k+c02c2m2 in the four-dimensional case, where k characterizes the horizon curvature and c2m2 is the coefficient of the second term of massive potential associated with the graviton mass.
• The positivity of such combination indicate the van der Waals-like phase transition.