Thermodynamics of Horndeski black holes with non-minimal derivative coupling

TL;DR

This paper investigates the thermodynamic properties and phase transitions of a novel class of Horndeski black holes with non-minimal derivative coupling, revealing rich behaviors influenced by electric charge and coupling strength.

Contribution

It introduces a new thermodynamic variable for Horndeski black holes and derives generalized laws, highlighting complex phase behavior and stability conditions.

Findings

Black holes exhibit two phase transitions with electric field presence.

Coupling strength acts as a thermodynamic pressure affecting stability.

Critical charge and cosmological parameters determine phase transition occurrence.

Abstract

We explore thermodynamic properties of a new class of Horndeski black holes whose action contains a non-minimal kinetic coupling of a massless real scalar and the Einstein tensor. Our treatment is based on the well-accepted consideration, where the cosmological constant is dealt with as thermodynamic pressure and the mass of black holes as thermodynamic enthalpy. We resort to a newly introduced intensive thermodynamic variable, i.e., the coupling strength of the scalar and tensor whose dimension is length square, and thus yield both the generalized first law of thermodynamics and the generalized Smarr relation. Our result indicates that this class of Horndeski black holes presents rich thermodynamic behaviors and critical phenomena. Especially in the case of the presence of an electric field, these black holes undergo two phase transitions. Once the charge parameter exceeds its critical value, or the cosmological parameter does not exceed its critical value, no phase transitions happen and the black holes are stable. As a by-product, we point out that the coupling strength acts as the thermodynamic pressure in the behavior of thermodynamics.