We study the general motion of photons in the Kerr-de Sitter black-hole
and naked singularity spacetimes. The motion is governed by the impact
parameters X, related to the axial symmetry of the spacetime, and q,
related to its hidden symmetry. Appropriate `effective potentials'
governing the latitudinal and radial motion are introduced and their
behavior is examined by the `Chinese boxes' technique giving regions
allowed for the motion in terms of the impact parameters. Restrictions
on the impact parameters X and q are established in dependence on the
spacetime parameters M, Λ , a. The motion can be of orbital type
(crossing the equatorial plane, q>0) and vortical type (tied above or
below the equatorial plane, q<0). It is shown that for negative
values of q, the reality conditions imposed on the latitudinal motion
yield stronger constraints on the parameter X than that following from
the reality condition of the radial motion, excluding the existence of
vortical motion of constant radius. The properties of the spherical
photon orbits of the orbital type are determined and used along with the
properties of the effective potentials as criteria of classification of
the KdS spacetimes according to the properties of the motion of the
photon.
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The study of quasi-periodic oscillations (QPOs) of X-ray flux observed
in the stellar-mass black hole binaries can provide a powerful tool for
testing of the phenomena occurring in the strong gravity regime.
Magnetized versions of the standard geodesic models of QPOs can explain
the observationally fixed data from the three microquasars. We perform a
successful fitting of the HF QPOs observed for three microquasars, GRS
1915+105, XTE 1550-564 and GRO 1655-40, containing black holes, for
magnetized versions of both epicyclic resonance and relativistic
precession models and discuss the corresponding constraints of
parameters of the model, which are the mass and spin of the black hole
and the parameter related to the external magnetic field. The estimated
magnetic field intensity strongly depends on the type of objects giving
the observed HF QPOs. It can be as small as 10^{-5} G if electron
oscillatory motion is relevant, but it can be by many orders higher for
protons or ions (0.02-1 G), or even higher for charged dust or such
exotic objects as lighting balls, etc. On the other hand, if we know by
any means the magnetic field intensity, our model implies strong limit
on the character of the oscillating matter, namely its specific charge.
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We study ultrahigh-energy particle collisions and optical effects in the
extraordinary class of mining braneworld Kerr-Newman (KN) naked
singularity spacetimes, predicting extremely high efficiency of
Keplerian accretion, and compare the results to those related to the
other classes of the KN naked singularity and black hole spacetimes. We
demonstrate that in the mining KN spacetimes the ultrahigh center-of-
mass energy occurs for collisions of particles following the extremely-
low-energy stable circular geodesics of the "mining regime," colliding
with large family of incoming particles, e.g., those infalling from the
marginally stable counter-rotating circular geodesics. This is
qualitatively different situation in comparison to the standard KN naked
singularity or black hole spacetimes where the collisional ultrahigh
center-of-mass energy can be obtained only in the near-extreme
spacetimes. We also show that observers following the stable circular
geodesics of the mining regime can register extremely blue-shifted
radiation incoming from the Universe, and see strongly deformed sky due
to highly relativistic motion along such stable orbits. The strongly
blue-shifted radiation could be thus a significant source of energy for
such orbiting observers.
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We provide a simple derivation of the corrections for Schwarzschild and
Schwarzschild-Tangherlini black hole entropy without knowing the details
of quantum gravity. We will follow the ideas of Bekenstein, Wheeler, and
Jaynes, using summation techniques without calculus approximations, to
directly find logarithmic corrections to the well-known entropy formula
for black holes. Our approach is free from pathological behavior giving
negative entropy for small values of black hole mass M . With the aid of
the "universality" principle, we will argue that this purely classical
approach could open a window for exploring properties of quantum
gravity.
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In our previous work (Paper I) we applied several models of high-
frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of
the central compact object in three Galactic microquasars assuming the
possibility that the central compact body is a super-spinning object (or
a naked singularity) with external spacetime described by Kerr geometry
with a dimensionless spin parameter a ≡ cJ/GM2 > 1. Here
we extend our consideration, and in a consistent way investigate
implications of a set of ten resonance models so far discussed only in
the context of a < 1. The same physical arguments as in Paper I are
applied to these models, I.e. only a small deviation of the spin
estimate from a = 1, a ≳ 1, is assumed for a favoured model. For five of
these models that involve Keplerian and radial epicyclic oscillations we
find the existence of a unique specific QPO excitation radius.
Consequently, there is a simple behaviour of dimensionless frequency M ×
νU(a) represented by a single continuous function having
solely one maximum close to a ≳ 1. Only one of these models is
compatible with the expectation of a ≳ 1. The other five models that
involve the radial and vertical epicyclic oscillations imply the
existence of multiple resonant radii. This signifies a more complicated
behaviour of M × νU(a) that cannot be represented by single
functions. Each of these five models is compatible with the expectation
of a ≳ 1.
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We study scalar and electromagnetic perturbations of a family of
nonsingular nonrotating black hole spacetimes that are solutions in a
large class of conformally invariant theories of gravity. The effective
potential for scalar perturbations depends on the exact form of the
scaling factor. Electromagnetic perturbations do not feel the scaling
factor, and the corresponding quasinormal mode spectrum is the same as
in the Schwarzschild metric. We find that these black hole metrics are
stable under scalar and electromagnetic perturbations. Assuming that the
quasinormal mode spectrum for scalar perturbations is not too different
from that for gravitational perturbations, we can expect that the
calculation of the quasinormal mode spectrum and the observation with
gravitational wave detectors of quasinormal modes from astrophysical
black holes can constrain the scaling factor and test these solutions.
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In Cardoso et al. [6] it was claimed that quasinormal modes which any
stationary, spherically symmetric and asymptotically flat black hole
emits in the eikonal regime are determined by the parameters of the
circular null geodesic: the real and imaginary parts of the quasinormal
mode are multiples of the frequency and instability timescale of the
circular null geodesics respectively. We shall consider asymptotically
flat black hole in the Einstein-Lovelock theory, find analytical
expressions for gravitational quasinormal modes in the eikonal regime
and analyze the null geodesics. Comparison of the both phenomena shows
that the expected link between the null geodesics and quasinormal modes
is violated in the Einstein-Lovelock theory. Nevertheless, the
correspondence exists for a number of other cases and here we formulate
its actual limits.
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In our previous work we applied several models of high-frequency quasi-
periodic oscillations to estimate the spin of the central compact object
in three Galactic microquasars. We also assumed the possibility that the
central compact body is a super-spinning object. Here we extend our
consideration and investigate in a consistent way the implications of
several resonance models so far discussed only in the context of black
holes.
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Conformal gravity can elegantly solve the problem of spacetime
singularities present in Einstein's gravity. For every physical
spacetime, there is an infinite family of conformally equivalent
singularity-free metrics. In the unbroken phase, every non-singular
metric is equivalent and can be used to infer the physical properties of
the spacetime. In the broken phase, a Higgs-like mechanism should select
a certain vacuum, which thus becomes the physical one. However, in the
absence of the complete theoretical framework we do not know how to
select the right vacuum. In this paper, we study the energy conditions
of non-singular black hole spacetimes obtained in conformal gravity
assuming they are solutions of Einstein's gravity with an effective
energy-momentum tensor. We check whether such conditions can be helpful
to select the vacuum of the broken phase.
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This comment is devoted to the recalculation of the Casimir energy of a
massless scalar field in the Kerr black hole surrounded by quintessence
derived in [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus
132, 98 (2017)] and its comparison with the results recently obtained in
[V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod.
Phys. Lett. A 32, 1750005 (2017)] in the spacetime [S. G. Ghosh, Eur.
Phys. J. C 76, 222 (2016)]. We have shown that in the more realistic
spacetime which does not have the failures illustrated here, the Casimir
energy is significantly bigger than that derived in [V. B. Bezerra, M.
S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A 32,
1750005 (2017)], and the difference becomes crucial especially in the
regions of near horizons of the spacetime.
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