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 (omega) 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 alpha = -e(2) not equal 0 and omega = 1/3, exactly as the Kerr-Newman black hole, and as the Kerr black hole when alpha = 0. Interestingly, for a given value of parameter omega, 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 omega and so is the ergoregion.