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 gravity considered as F(R,T)=R+βT theory with the addition of a matter term, so gravitational Lagrangian is resemblant Einstein general relativity. In fact, resulting central term coincident relativity since T only trace term. then exhibit entropy from CFT this equivalent Bekenstein–Hawking no correction related coupling constant. Moreover, when constant κλ switched off and approaching zero, we may extend 5D solution. It found extremal contains twofold duals call Q-picture P-picture. both pictures, reproduces exactly for Reissner–Nordström quintessence. The results establish that, all holes quintessence, microscopic entropies dual CFTs agree entropies.