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 $$\alpha =-e^2 \ne 0$$ 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.

Перевод пока недоступен