CFT Duals on Rotating Charged Black Holes Surrounded by Quintessence

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 $F(R,T) = R + \beta T$ theory with the addition of a matter term, so the gravitational Lagrangian is resemblant to Einstein general relativity. In fact, the resulting central term is coincident to the central term in the general relativity since $T$ is only a trace of the matter term. We then exhibit 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 $\kappa \lambda$ is switched off and $a$ is approaching zero, we may extend the solution to the 5D black hole solution. It is found that this extremal 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-Nordstr\"om 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.