Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory

TL;DR

This paper investigates the thermodynamics of charged black holes in Einstein-Horndeski-Maxwell theory, revealing an additional contribution to the first law due to scalar field behavior and exploring viscosity bounds in dual theories.

Contribution

It extends previous uncharged black hole thermodynamics studies by including electromagnetic fields, demonstrating the necessity of an extra term in the first law and analyzing viscosity ratios.

Findings

Extra contribution in the first law due to scalar field horizon behavior

Violation of the viscosity bound depending on mass and charge

Derived thermodynamic constraints for charged black holes in various dimensions

Abstract

We extend an earlier investigation of the thermodynamics of static black holes in an Einstein-Horndeski theory of gravity coupled to a scalar field, by including now an elec- tromagnetic field as well. By studying the two-parameter families of charged static black holes, we obtain much more powerful constraints on the thermodynamics since, unlike in the uncharged one-parameter case, now the right-hand side of the first law is not automatically integrable. In fact, this allows us to demonstrate that there must be an additional contribution in the first law, over and above the usual terms expected for charged black holes. The origin of the extra contribution can be attributed to the behaviour of the scalar field on the horizon of the black hole. We carry out the calculations in four dimensions and also in general dimensions. We also derive the ratio of viscosity to entropy for the dual boundary field theory, showing that the usual viscosity bound for isotropic solutions can be violated, with the ratio depending on the mass and charge.