CFT Duals on Rotating Charged Black Holes Surrounded by Quintessence

Abstract

We demonstrate that Kerr/CFT duality can be extended to rotating charged black hole solution surrounded by quintessence in Rastall gravity. Since Rastall gravity can be considered as F (R, T ) = R + βT theory with a matter term, so the gravitational Lagrangian is similar to Einstein general relativity. In fact, the resulting central term is similar to the general relativity since T is only a trace of the matter term. We then show that the entropy from CFT of this black hole is equivalent with the Bekenstein-Hawking entropy with no correction related to the Rastall coupling constant. Moreover, when Rastall coupling constant κλ is switched off and a is approaching zero, we may extend the solution to 5D black hole solution. It is found that this solution contains twofold CFT duals that we call as Q-picture and P -picture. In both pictures, the CFT entropy reproduces exactly the Bekenstein-Hawking entropy for Reissner-Nordström black hole surrounded by quintessence. The results establish that, for all black holes surrounded by quintessence, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies.