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;