Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field

Abstract

In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.

10 pages (two columns format), 10 figures, some references added, titles of references added

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• Dilaton black holes with power law electrodynamics
• Effects of power-law Maxwell field on the Van der Waals like phase transition of higher dimensional dilaton black holes
• Black hole solutions in Gauss-Bonnet-massive gravity in the presence of power-Maxwell field
• Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics
• Holographic conductivity in the massive gravity with power-law Maxwell field
• Alternative approach to the critical behavior and microscopic structure of the power-Maxwell black holes
• Holographic DC Conductivity for a Power-law Maxwell Field
• Entropic force between two horizons of dilaton black holes with a power-Maxwell field
• Charged quantum Oppenheimer-Snyder model
• Thermodynamics of charged black holes in Maxwell-dilaton-massive gravity
• Holographic paramagnetic-ferromagnetic phase transition of Power-Maxwell-Gauss-Bonnet black holes