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–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.

我们证明了Kerr / CFT对偶性可以扩展到由Rastall重力中的典型包围的旋转带电黑洞解决方案。由于拉斯塔尔重力可以被认为是$F（\mathrm{[R}，Ť）=\mathrm{[R}+\beta Ť$引力的拉格朗日理论与爱因斯坦广义相对论相似。实际上，所得的中心项与广义相对论的中心项重合，因为$Ť$只是这个问题术语的痕迹。然后，我们证明该黑洞的CFT熵与Bekenstein-Hawking熵等效，而与Rastall耦合常数无关。而且，当拉斯塔尔耦合常数$\kappa \lambda$ 关闭并 $\mathrm{一个}$接近零，我们可以将解决方案扩展到5D黑洞解决方案。发现该极值解包含双重CFT对偶，我们称之为$问$图片和 $P$-图片。在两张图片中，CFT熵精确地再现了被精粹包围的Reissner-Nordström黑洞的Bekenstein-Hawking熵。结果表明，对于所有被精髓包围的黑洞，双重CFT的微观熵与Bekenstein-Hawking熵一致。