**Publication date:** Dec 2015

**Abstract:**

Quintessential dark energy with density $rho$ and pressure $p$ is

governed by an equation of state of the form $p=-omega_{q}rho$ with

the quintessential parameter $omega_qin(-1;-1/3)$. We derive the

geometry of quintessential rotating black holes, generalizing thus the

Kerr spacetimes. Then we study the quintessential rotating black hole

spacetimes with the special value of $omega_q = -2/3$ when the

resulting formulae are simple and easily tractable. We show that such

special spacetimes can exist for dimensionless quintessential parameter

$c<1/6$ and determine the critical rotational parameter $a_0$

separating the black hole and naked singularity spacetime in dependence

on the quintessential parameter $c$. For the spacetimes with $omega_q =

2/3$ we present the integrated geodesic equations in separated form and

study in details the circular geodetical orbits. We give radii and

parameters of the photon circular orbits, marginally bound and

marginally stable orbits. We stress that the outer boundary on the

existence of circular geodesics, given by the so called static radius

where the gravitational attraction of the black hole is balanced by the

cosmic repulsion, does not depend on the dimensionless spin of the

rotating black hole, similarly to the case of the Kerr-de Sitter

spacetimes with vacuum dark energy. We also give restrictions on the

dimensionless parameters $c$ and $a$ of the spacetimes allowing for

existence of stable circular geodesics.

**Authors:**

Toshmatov, Bobir; Stuchlík, Zdeněk; Ahmedov, Bobomurat;