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

As we knowthat 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 general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in EinsteinGauss- Bonnet gravity surrounded by the quintessence matter, and we 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 a 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 (>) over bar) r(C).