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 $\alpha =-e^2\mathrm{\ne }0$ and $\omega =1\mathrm{/}3$, 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.