Quintessence background for $5D$ Einstein-Gauss-Bonnet black holes

TL;DR

This paper derives a five-dimensional Einstein-Gauss-Bonnet black hole solution surrounded by quintessence matter, analyzing its thermodynamics and phase transitions, revealing corrected thermodynamic quantities and stability conditions.

Contribution

It presents a novel 5D black hole solution in Einstein-Gauss-Bonnet gravity with quintessence, including thermodynamic analysis and phase transition characterization.

Findings

Thermodynamic quantities are corrected by quintessence effects.

Phase transition occurs at a specific radius with a discontinuity in specific heat.

Stable and unstable black hole branches are identified based on size.

Abstract

As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first and the second order terms correspond to the general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a $5D$ black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and phase transition is achievable. The phase transition for the thermodynamic stability, is characterized by a discontinuity in the specific heat at $r=r_C$, with the stable (unstable) branch for $r < (>) r_C$.