Rotating black hole and quintessence

We discuss spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, which has an additional parameter (ω ) due to the quintessential matter, apart from the mass ( M). In turn, we employ the Newman-Janis complex transformation to this spherical quintessence black hole solution and present a rotating counterpart that is identified, for α =-e^2 ≠ 0 and ω =1/3, exactly as the Kerr-Newman black hole, and as the Kerr black hole when α =0. Interestingly, for a given value of parameter ω , there exists a critical rotation parameter (a=a_E), which corresponds to an extremal black hole with degenerate horizons, while for a<a_E, it describes a non-extremal black hole with Cauchy and event horizons, and no black hole for a>a_E. We find that the extremal value a_E is also influenced by the parameter ω and so is the ergoregion.