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.
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We study the shadow of the rotating black hole with quintessential
energy i) in vacuum and ii) in the presence of plasma with radial
power-law density. For vacuum case the quintessential field parameter of
the rotating black hole sufficiently changes the shape of the shadow.
With the increasing the quintessential field parameter the radius of the
shadow also increases. With the increase of the radius of the shadow of
the rotating black hole the quintessential field parameter causes
decrease of the distortion of the shadow shape: In the presence of the
quintessential field parameter the shadow of fast rotating black hole
starting to become more close to circle. The shape and size of shadow of
quintessential rotating black hole surrounded by plasma depends on i)
plasma parameters, ii) black hole spin and iii) quintessential field
parameter. With the increase of the plasma refraction index the apparent
radius of the shadow increases. However, for the big values of the
quintessential field parameter the change of the black hole shadow's
shape due to the presence of plasma is not sufficient. In other words:
the effect of the quintessential field parameter becomes more dominant
with compare to the effect of plasma.
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In this paper, we study circular geodesic motion of test particles and
photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing
spherically symmetric regular black-hole or no-horizon spacetimes. While
the Bardeen geometry is not exact solution of Einstein's equations, the
ABG spacetime is related to self-gravitating charged sources governed by
Einstein's gravity and nonlinear electrodynamics. They both are
characterized by the mass parameter m and the charge parameter g. We
demonstrate that in similarity to the Reissner-Nordstrom (RN) naked
singularity spacetimes an antigravity static sphere should exist in all
the no-horizon Bardeen and ABG solutions that can be surrounded by a
Keplerian accretion disc. However, contrary to the RN naked singularity
spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can
contain also an additional inner Keplerian disc hidden under the static
antigravity sphere. Properties of the geodesic structure are reflected
by simple observationally relevant optical phenomena. We give silhouette
of the regular black-hole and no-horizon spacetimes, and profiled
spectral lines generated by Keplerian rings radiating at a fixed
frequency and located in strong gravity region at or nearby the
marginally stable circular geodesics. We demonstrate that the profiled
spectral lines related to the regular black-holes are qualitatively
similar to those of the Schwarzschild black-holes, giving only small
quantitative differences. On the other hand, the regular no-horizon
spacetimes give clear qualitative signatures of their presence while
compared to the Schwarschild spacetimes. Moreover, it is possible to
distinguish the Bardeen and ABG no-horizon spacetimes, if the
inclination angle to the observer is known.
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We have studied the orbits of magnetized particles around Hořava-Lifshitz black hole with mass M immersed in an asymptotically uniform magnetic field in the infrared approximation when ω M2≫ 1. It is shown that magnetized particle's orbit in Hořava-Lifshitz spacetime is different with compare to one in Schwarzschild spacetime due to the presence of additional terms related to the Kehagias-Sfetsos (KS) parameter ω. Using the Hamilton-Jacobi formalism, we have found the dependence of the area of stable circular orbits of the magnetized particle on dimensionless KS parameter tilde{ω} and have plotted them for several values of magnetic coupling parameter β as well as obtained the equations of motion of the magnetized particle. Moreover, we have studied the dependence of the collision of (magnetized, charged, non-charged) particles on KS parameter ω for some fixed values of the magnetic coupling parameter β.
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Possible astrophysical consequences of the Hořava quantum gravity theory have been recently studied by several authors. They usually employ the Kehagias-Sfetsos (KS) spacetime which is a spherically symmetric vacuum solution of a specific version of Hořava's gravity. The KS metric has several unusual geometrical properties that in the present article we examine by means of the often used technique of embedding diagrams. We pay particular attention to the transition between naked singularity and black-hole states, which is possible along some particular sequences of the KS metrics.
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We have studied the orbits of magnetized particles around
Hořava-Lifshitz black hole with mass M immersed in an
asymptotically uniform magnetic field in the infrared approximation when
ω M2≫ 1. It is shown that magnetized particle's
orbit in Hořava-Lifshitz spacetime is different with compare to
one in Schwarzschild spacetime due to the presence of additional terms
related to the Kehagias-Sfetsos (KS) parameter ω. Using the
Hamilton-Jacobi formalism, we have found the dependence of the area of
stable circular orbits of the magnetized particle on dimensionless KS
parameter tilde{ω} and have plotted them for several values of
magnetic coupling parameter β as well as obtained the equations of
motion of the magnetized particle. Moreover, we have studied the
dependence of the collision of (magnetized, charged, non-charged)
particles on KS parameter ω for some fixed values of the magnetic
coupling parameter β.
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Possible astrophysical consequences of the Hořava quantum gravity
theory have been recently studied by several authors. They usually
employ the Kehagias-Sfetsos (KS) spacetime which is a spherically
symmetric vacuum solution of a specific version of Hořava's
gravity. The KS metric has several unusual geometrical properties that
in the present article we examine by means of the often used technique
of embedding diagrams. We pay particular attention to the transition
between naked singularity and black-hole states, which is possible along
some particular sequences of the KS metrics.
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We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.
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We construct perfect fluid tori in the field of the Kehagias-Sfetsos
(K-S) naked singularities. These are spherically symmetric vacuum
solutions of the modified Hořava quantum gravity, characterized
by a dimensionless parameter ω M^2, combining the gravitational
mass parameter M of the spacetime with the Hořava parameter
ω reflecting the role of the quantum corrections. In dependence on
the value of ω M^2, the K-S naked singularities demonstrate a
variety of qualitatively different behavior of their circular geodesics
that is fully reflected in the properties of the toroidal structures,
demonstrating clear distinction to the properties of the torii in the
Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes
the tori are located above an "antigravity" sphere where matter can stay
in a stable equilibrium position, which is relevant for the stability of
the orbiting fluid toroidal accretion structures. The signature of the
K-S naked singularity is given by the properties of marginally stable
tori orbiting with the uniform distribution of the specific angular
momentum of the fluid, l= const. In the K-S naked singularity spacetimes
with ω M^2 > 0.2811, doubled tori with the same l= const can
exist; mass transfer between the outer torus and the inner one is
possible under appropriate conditions, while only outflow to the outer
space is allowed in complementary conditions. In the K-S spacetimes with
ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not
possible due to the non-existence of unstable circular geodesics.
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In order to test the role of large-scale magnetic fields in quasi-periodic oscillation phenomena observed in microquasars, we study the oscillatory motion of charged particles in the vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole and the strength of the magnetic field. We demonstrate that assuming relevance of resonant phenomena of the radial and latitudinal oscillations of charged particles at their frequency ratio $3;:2$ 3 : 2 , the oscillatory frequencies of charged particles can be well related to the frequencies of the twin high-frequency quasi-periodic oscillations observed in the microquasars GRS 1915+105, XTE 1550-564 and GRO 1655-40.
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