Rotating black hole and quintessence

Abstract

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 \(\alpha=-e^2 \neq 0\) 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.