Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories

TL;DR

This paper constructs exact non-linear charged black hole solutions in a four-dimensional Scalar-Gauss-Bonnet theory with matter, analyzing their thermodynamics and stability, and confirming a Smarr relation.

Contribution

It introduces new exact hairy black hole solutions with non-linear electrodynamics in a 4D Scalar-Gauss-Bonnet framework, extending previous models.

Findings

Black holes have finite thermodynamic quantities despite relaxed asymptotics

Identified stable regions under thermal and electrical fluctuations

Confirmed Smarr relation for these black hole solutions

Abstract

In this work, we consider the recently proposed well-defined theory that permits a healthy $D\to 4$ limit of the Einstein-Gauss-Bonnet combination, which requires the addition of a scalar degree of freedom. We continue the construction of exact, hairy black hole solutions in this theory in the presence of matter sources, by considering a nonlinear electrodynamics source, constructed through the Pleba\'nski tensor and a precise structural function $\mathcal{H}(P)$. Computing the thermodynamic quantities with the Wald formalism, we identify a region in parameter space where the hairy black holes posses well-defined, non-vanishing, finite thermodynamic quantities, in spite of the relaxed asymptotic approach to planar AdS. We test its local stability under thermal and electrical fluctuations and we also show that a Smarr relation is satisfied for these black hole configurations.