Rotating black hole and quintessence

TL;DR

This paper derives and analyzes rotating black hole solutions in quintessence matter, revealing how parameters like  and  influence extremality, horizons, and ergoregions, extending classical Kerr solutions.

Contribution

It introduces a rotating black hole solution with quintessential matter, generalizing Kerr-Newman black holes, and explores the effects of quintessence parameters on black hole properties.

Findings

Existence of a critical rotation parameter for extremal black holes.

Dependence of horizons and ergoregion size on quintessence parameters.

Extension of Kerr-Newman solutions to include quintessential matter.

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.