Here we show that the phenomenon of arbitrarily long-lived quasinormal
modes (called quasiresonances) of a massive scalar field in the vicinity
of a black hole is not an artifact of the test field approximation, but
takes place also when the (derivative) coupling of a scalar field with
the Einstein tensor is taken into consideration. We observe that at
large coupling and high multipole numbers, the growing modes appear in
the spectrum, which are responsible for the eikonal instability of the
field. For small coupling, when the configuration is stable, there
appear the purely imaginary quasinormal modes which are nonperturbative
in the coupling constant. At the sufficiently small coupling the
nonminimal scalar field is stable and the asymptotic late-time tails are
not affected by the coupling term. The accurate calculations of
quasinormal frequencies for a massive scalar field with the derivative
coupling in the Reissner-Nordström black-hole background are performed
with the help of the Frobenius method, time-domain integration and WKB
expansion.
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An exact solution of the Lemaître-Tolman-Bondi class is investigated as
a possible model of the Schwarzschild-like black hole embedded in a
nonstatic dust-filled universe for the three types of spatial curvature.
The solution is obtained in comoving coordinates by means of the mass
function method. It is shown that the central part of space contains a
Schwarzschild-like black hole. The R-T structure of the resulting
spacetime is built. It is shown that the solution includes both the
Schwarzschild and Friedmann solutions as its natural limits. The
geodesic equations for test particles are analyzed. The particle
observable velocities are found. The trajectories of the test particles
are built from the point of view of both comoving and distant observers.
For the distant observer, the results coincide with the Schwarzschild
picture within a second-order accuracy near the symmetry center.
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We investigate how a spherically symmetric scalar field can modify the
Schwarzschild vacuum solution when there is no exchange of energy-
momentum between the scalar field and the central source of the
Schwarzschild metric. This system is described by means of the
gravitational decoupling by Minimal Geometric Deformation (MGD-
decoupling), which allows us to show that, under the MGD paradigm, the
Schwarzschild solution is modified in such a way that a naked
singularity appears.
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The exact axisymmetric and static solution of the Einstein equations
coupled to the axisymmetric and static gravitating scalar (or phantom)
field is presented. The spacetimes modified by the scalar field are
explicitly given for the so-called γ -metric and the Erez-Rosen metric
with quadrupole moment q , and the influence of the additional
deformation parameters γ* and q* generated by the
scalar field is studied. It is shown that the null energy condition is
satisfied for the phantom field, but it is not satisfied for the
standard scalar field. The test particle motion in both the modified γ
-metric and the Erez-Rosen quadrupole metric is studied; the circular
geodesics are determined, and near-circular trajectories are explicitly
presented for characteristic values of the spacetime parameters. It is
also demonstrated that the parameters γ* and q*
have no influence on the test particle motion in the equatorial plane.
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The axial electromagnetic (EM) perturbations of the black hole (BH)
solutions in general relativity coupled to nonlinear electrodynamics
(NED) were studied for both electrically and magnetically charged BHs,
assuming that the EM perturbations do not alter the spacetime geometry
in our preceding paper [Phys. Rev. D 97, 084058 (2018),
10.1103/PhysRevD.97.084058]. Here, as a continuation of that work, the
formalism for the polar EM perturbations of the BHs in general
relativity coupled to the NED is presented. We show that the quasinormal
modes (QNMs) spectra of polar EM perturbations of the electrically and
magnetically charged BHs in the NED are not isospectral, contrary to the
case of the standard Reissner-Nordström BHs in the classical linear
electrodynamics. It is shown by the detailed study of QNMs properties in
the eikonal approximation that the EM perturbations can be a powerful
tool to confirm that in the NED light ray does not follow the null
geodesics of the spacetime. By specifying the NED model and comparing
axial and polar EM perturbations of the electrically and magnetically
charged BHs, it is shown that QNM spectra of the axial EM perturbations
of magnetically (electrically) charged BH and polar EM perturbations of
the electrically (magnetically) charged BH are isospectral, i.e.,
ωmagax≈ωelpol
(ωmagpol≈ωelax).
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There is strong observational evidence that many active galactic nuclei
(AGNs) harbour super-massive black holes (SMBHs), demonstrating multi-
accretion episodes during their life-time. In such AGNs, corotating and
counterrotating tori, or strongly misaligned disks, as related to the
central Kerr SMBH spin, can report traces of the AGNs evolution. Here we
concentrate on aggregates of accretion disks structures, ringed
accretion disks (RADs) orbiting a central Kerr SMBH, assuming that each
torus of the RADs is centered in the equatorial plane of the attractor,
tori are coplanar and axi-symmetric. Many of the RAD aspects are
governed mostly by the spin of the Kerr geometry. We classify Kerr black
holes (BHs) due to their dimensionless spin, according to possible
combinations of corotating and counterrotating equilibrium or unstable
(accreting) tori composing the RADs. The number of accreting tori in
RADs cannot exceed n = 2. We present list of 14 characteristic values
of the Kerr BH dimensionless spin a governing the classification in
whole the black hole range , uniquely constrained by the RAD properties.
The spin values are remarkably close providing an accurate
characterization of the Kerr attractors based on the RAD properties. RAD
dynamics is richer in the spacetimes of high spin values. One of the
critical predictions states that a RAD tori couple formed by an outer
accreting corotating and an inner accreting counterrotating torus is
expected to be observed only around slowly spinning (a < 0.46M)
BHs. The analysis strongly binds the fluid and BH characteristics
providing indications on the situations where to search for RADs
observational evidences. Obscuring and screening tori, possibly evident
as traces in x-ray spectrum emission, are strongly constrained,
eventually ruling out many assumptions used in the current
investigations of the screening effects. We expect relevance of our
classification of Kerr spacetimes in relation to astrophysical phenomena
arising in different stages of AGNs life that could be observed by the
planned x-ray satellite observatory ATHENA (Advanced Telescope for High
ENergy Astrophysics).
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In many astrophysically relevant situations, radiation-reaction forces
acting upon a charge cannot be ignored, and the question of the location
and stability of circular orbits in such a regime arises. The motion of
a point charge with radiation reaction in flat spacetime is described by
the Lorenz-Dirac (LD) equation, while in curved spacetime it is
described by the DeWitt-Brehme (DWB) equation containing the Ricci term
and a tail term. We show that for the motion of elementary particles in
vacuum metrics, the DWB equation can be reduced to the covariant form of
the LD equation, which we use here. Generically, the LD equation is
plagued by runaway solutions, so we discuss computational ways of
avoiding this problem when constructing numerical solutions. We also use
the first iteration of the covariant LD equation, which is the covariant
Landau-Lifshitz equation, comparing the results of these two approaches
and showing the smallness of the third-order Schott term in the
ultrarelativistic case. We calculate the corresponding energy and
angular momentum loss of a particle and study the damping of charged
particle oscillations around an equilibrium radius. We find that,
depending on the orientation of the Lorentz force, the oscillating
charged particle either spirals down to the black hole or stabilizes the
circular orbit by decaying its oscillations. The latter case leads to
the interesting new result of the particle orbit shifting outwards from
the black hole. We also discuss the astrophysical relevance of the
presented approach and provide estimates of the main parameters of the
model.
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Charged fluids circling in strong central gravitational and ambinet
magnetic fields, characteristic for compact objects backgrounds, can
embody interesting configurations. In contrast to the widely considered
neutral fluid structures imitating thick equatorial accretion discs with
negligible loss of mass, when the fluid is properly charged, we can find
it forming unique toroidal structures `levitating' above the equatorial
plane and also those hovering near the symmetry axis. Along with
analytical topological studies of these structures, we can also present
an survey of their basic physical characteristics, such as pressure,
density and temperature profiles.
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We discuss the photon motion in the framework of general relativity
coupled to non-linear electrodynamics. Photons no longer follow the
null-geodesics of the spacetime but rather null-geodesics of associated
effective metric. Here we compare structure of circular geodesics and
time-delays of neutrinos in Bardeen spacetimes with those of photons in
effective geometry. We also discuss construction the Keplerian disks
images in the Bardeen spacetimes and compare them with the images of
Keplerian disks in RN spacetime.
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We discuss in the framework of general relativity the role of the dark
energy represented by the cosmological constant, restricted due to
cosmological tests, in the polytropic models of dark matter halos. The
internal spacetime of the polytropic spheres governs circular geodesic
orbits that can be compared with the velocity curves observed in large
galaxies, indicating the possibility to use for the halo model both non-
relativistic very extended and diluted polytropes, or relativistic
polytropes with nearly critical value of the relativistic parameter
sigma = p_mathrm{c}/varrho_mathrm{c} enabling extremely large polytrope
extension, limited efficiently by the influence of the dark energy to
agree with extension of dark matter halos of large galaxies. We also
show that the so-called trapping relativistic polytropes with extremely
large extension allow for gravitational instability of their central
parts leading to the creation of a supermassive black hole inside of
such an extremely extended polytrope representing galactic halo.
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