Charged solution with equal metric ansatz in Gauss-Bonnet theory coupled to scalar field

TL;DR

This paper derives a new charged black hole solution in Gauss-Bonnet gravity coupled with a scalar field, revealing additional terms affecting black hole properties and thermodynamics compared to the classical Reissner-Nordström solution.

Contribution

It introduces a novel spherically symmetric charged black hole solution with equal metric components in Gauss-Bonnet theory coupled to a scalar field, including detailed analysis of its properties and thermodynamics.

Findings

Additional terms of order 1/r^6 and 1/r^9 compared to Reissner-Nordström black hole.

Scalar field influences the structure and horizon properties of the black hole.

Modified first law of thermodynamics and Smarr relation due to scalar-Gauss-Bonnet coupling.

Abstract

In the course of this research, we employ the Gauss-Bonnet equation of motion alongside the scalar field and potential to acquire a fresh solution for a spherically symmetrical charged black hole. Specifically, we derive this black hole solution by employing a metric potential where the components are equal, that is, $g_{tt}=g_{rr}$. In our research, we achieve several accomplishments, including fixing the characteristics of the scalar field, and the Gauss-Bonnet term. We thoroughly examine the physical properties associated with such black hole and show that we have supplementary terms when compared to the Reissner-Nordstr\"om black hole solution. These additional terms are of the order $O(\frac{1}{r^6})$ and $O(\frac{1}{r^9})$. The presence of these supplementary terms can be attributed to the impact of the scalar function denoted as $\xi$. Such expressions play a crucial role in generating the multi-horizon black hole solution. The presence of these extra terms facilitates the derivation of a modified first law of thermodynamics and the corresponding Smarr relation.