**Publication date:** Feb 2017

**Abstract:**

Quintessential dark energy with density ρ and pressure p is governed by

an equation of state of the form p=ω_{q}ρ with the

quintessential parameter ω_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 ω_{q} = -2/3 when the

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

special spacetimes can exist for the 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 ω_{q} = -2/3 we give all the black hole characteristics and

demonstrate local thermodynamical stability. 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. Finally, using

numerical methods we generalize the discussion of the circular geodesics

to the black holes with arbitrary quintessential parameter

ω_{q}.

**Authors:**

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