Topological black hole chemistry in massive gravity with power-Maxwell invariant field

Abstract

In this paper, asymptotically AdS black hole solutions of massive gravity in the presence of nonlinear electromagnetic field arisen from the power theory of Maxwell invariant are investigated and the associated Euclidean on-shell action is presented. Using the Euclidean on-shell action, the gravitational partition function in the canonical ensemble is computed in arbitrary dimensions and then thermodynamic quantities of topological black holes are obtained. By extending the thermodynamic phase space, i.e., treating negative cosmological constant as thermodynamic pressure, the first law of thermodynamics as well as associated Smarr formula are examined. Next, the equation of state of topological black holes is obtained and it is proven that the critical point equation of these solutions can exhibit black hole phase transitions similar to those of van der Waals, van der Waals like and solid/liquid/gas (related to triple point) phase transitions in usual thermodynamic systems. Especially, the van der Waals phase transition is observed in 4 and higher dimensions, van der Waals type phase transition can be seen in 6 and higher dimensions, and phase transitions associated with triple point, i.e., small/intermediate/large black hole phase transition may happen in 6 and higher dimensions.