Kerr–Newman–NUT–Kiselev black holes in Rastall theory of gravity and Kerr/CFT correspondence

We present a new twisted rotating black hole solution by performing Demiański–Newman–Janis algorithm to the electrically and dyonically charged black hole with quintessence in Rastall theory of gravity. Using our black hole solution, we argue that Rastall gravity is not equivalent with Einstein gravity. For further explanation, the black hole properties such as the horizon and ergosphere are studied for which there are some different properties for those theories. Some thermodynamic properties of the black hole solution are also discussed. At the end, considering the Kerr/CFT correspondence is valid for our black hole solution, the central charge from the CFT of this extremal solution is derived. •Rotating, twisting, charged black hole with quintessence in Rastall theory.•Kerr–Newman–NUT–Kiselev black hole solution in Rastall gravity.•Bekenstein–Hawking entropy for Kerr–Newman–NUT–Kiselev black hole.•The left-moving central charge depends on the quintessential intensity.•Left-moving temperature of Kerr–Newman–NUT black hole.