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

Abstract

In this study, we apply the Gauss–Bonnet equation of motions coupled with the scalar field and potential and derive a new charged spherically symmetric black hole (BH) solution. In this study, we derive this BH using an equal metric potential, i.e., gtt=grr. Among many things, we succeed in determining the form of the scalar field, the function of the scalar, and the Gauss–Bonnet term. We investigate the physics of this BH solution and show that we have additional terms than the Riessner Nordström BH solution, i.e., O(1r6) and O(1r9). The existence of these additional terms is due to the contribution of the scalar field ξ. These additional terms are responsible for reproducing the multi-horizon BH solution. Due to the existence of these additional terms, the modified first law of thermodynamics and the corresponding Smarr relation are derived.