Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray
power-density spectra of several accreting low-mass neutron star (NS)
binaries. In our previous work we have considered several QPO models. We
have identified and explored mass-angular-momentum relations implied by
individual QPO models for the atoll source 4U 1636-53. In this paper we
extend our study and confront QPO models with various NS equations of
state (EoS). We start with simplified calculations assuming Kerr
background geometry and then present results of detailed calculations
considering the influence of NS quadrupole moment (related to
rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes.
We show that the application of concrete EoS together with a particular
QPO model yields a specific mass-angular-momentum relation. However, we
demonstrate that the degeneracy in mass and angular momentum can be
removed when the NS spin frequency inferred from the X-ray burst
observations is considered. We inspect a large set of EoS and discuss
their compatibility with the considered QPO models. We conclude that
when the NS spin frequency in 4U 1636-53 is close to 580 Hz, we can
exclude 51 of the 90 considered combinations of EoS and QPO models. We
also discuss additional restrictions that may exclude even more
combinations. Namely, 13 EOS are compatible with the observed twin-peak
QPOs and the relativistic precession model. However, when considering
the low-frequency QPOs and Lense-Thirring precession, only 5 EOS are
compatible with the model.
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Spherically symmetric equilibrium configurations of perfect fluid
obeying a polytropic equation of state are studied in spacetimes with a
repulsive cosmological constant. The configurations are specified in
terms of three parameters—the polytropic index n , the ratio of central
pressure and central energy density of matter σ , and the ratio of
energy density of vacuum and central density of matter λ . The static
equilibrium configurations are determined by two coupled first-order
nonlinear differential equations that are solved by numerical methods
with the exception of polytropes with n =0 corresponding to the
configurations with a uniform distribution of energy density, when the
solution is given in terms of elementary functions. The geometry of the
polytropes is conveniently represented by embedding diagrams of both the
ordinary space geometry and the optical reference geometry reflecting
some dynamical properties of the geodesic motion. The polytropes are
represented by radial profiles of energy density, pressure, mass, and
metric coefficients. For all tested values of n >0 , the static
equilibrium configurations with fixed parameters n , σ , are allowed
only up to a critical value of the cosmological parameter
λc=λc(n ,σ ). In the case of n >3 , the
critical value λc tends to zero for special values of σ . The
gravitational potential energy and the binding energy of the polytropes
are determined and studied by numerical methods. We discuss in detail
the polytropes with an extension comparable to those of the dark matter
halos related to galaxies, i.e., with extension ℓ>100 kpc and mass M
>1 012 M☉ . For such largely extended
polytropes, the cosmological parameter relating the vacuum energy to the
central density has to be larger than λ
=ρvac/ρc̃10-9. We demonstrate that the
extension of the static general relativistic polytropic configurations
cannot exceed the so-called static radius related to their external
spacetime, supporting the idea that the static radius represents a
natural limit on the extension of gravitationally bound configurations
in an expanding universe dominated by the vacuum energy.
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We study optical effects in quintessential Kerr black hole spacetimes
corresponding to the limiting case of the equation-of-state parameter ω
q=-1/3 of the quintessence. In dependence on the
dimensionless quintessential field parameter c, we determine the black
hole silhouette and the spectral line profiles of Keplerian disks
generated in this special quintessential Kerr geometry, representing an
extension of the general modifications of the Kerr geometry introduced
recently by Ghasemi-Nodehi and Bambi (Eur. Phys. J. C 56:#290, 2016). We
demonstrate that due to the influence of the parameter c, the silhouette
is almost homogeneously enlarged, and the spectral line profiles are
redshifted with almost conserved shape.
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In this work we have obtained the set of new exact solutions of the
Einstein equations that generalize the known Lemaitre-Tolman-Bondi
solution for the certain case of nonzero pressure under zero spatial
curvature. These solutions are pretending to describe the black hole
immersed in the nonstatic cosmological background and give a possibility
to investigate the problems concerning the effects of the cosmological
expansion in gravitationally bounded systems. They may also be used as a
seed models in the problem of structure formation in the universe at the
epoch of matter and radiation decoupling. It was shown that each of the
solutions obtained contains either the Reissner-Nordstrom or the
Schwarzschild black hole in the central region of the space. It is
demonstrated that the approach of the mass function use in solving the
Einstein equations allows clear physical interpretation of the resulting
solutions that is of much benefit to any their further application.
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In this work we have obtained the set of new exact solutions of Einstein
equations that generalize the known LTB solution for the particular case
of nonzero pressure under zero spatial curvature. These solutions are
pretending to describe the black hole immersed in nonstatic cosmological
background and give a possibility to investigate the hot problems
concerning the effects of the cosmological expansion in gravitationally
bounded systems and other related problems. It was shown that each of
the solutions obtained contains either the Reissner-Nordstrom or the
Schwarzschild black hole in the central region of the space. It is
demonstrated that the approach of the mass function use in solving the
Einstein equations allows clear physical interpretation of the resulting
solutions that is of much benefit to any their concrete application.
Read More
Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray
power-density spectra of several accreting low-mass neutron star (NS)
binaries. In our previous work we have considered several QPO models. We
have identified and explored mass-angular-momentum relations implied by
individual QPO models for the atoll source 4U 1636-53. In this paper we
extend our study and confront QPO models with various NS equations of
state (EoS). We start with simplified calculations assuming Kerr
background geometry and then present results of detailed calculations
considering the influence of NS quadrupole moment (related to
rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes.
We show that the application of concrete EoS together with a particular
QPO model yields a specific mass-angular-momentum relation. However, we
demonstrate that the degeneracy in mass and angular momentum can be
removed when the NS spin frequency inferred from the X-ray burst
observations is considered. We inspect a large set of EoS and discuss
their compatibility with the considered QPO models. We conclude that
when the NS spin frequency in 4U 1636-53 is close to 580Hz we can
exclude 51 from 90 of the considered combinations of EoS and QPO models.
We also discuss additional restrictions that may exclude even more
combinations. Namely, there are 13 EOS compatible with the observed twin
peak QPOs and the relativistic precession model. However, when
considering the low frequency QPOs and Lense-Thirring precession, only 5
EOS are compatible with the model.
Read More
Spherically symmetric equilibrium configurations of perfect fluid
obeying a polytropic equation of state are studied in spacetimes with a
repulsive cosmological constant. The configurations are specified in
terms of three parameters---the polytropic index $n$, the ratio of
central pressure and central energy density of matter $sigma$, and the
ratio of energy density of vacuum and central density of matter
$lambda$. The static equilibrium configurations are determined by two
coupled first-order nonlinear differential equations that are solved by
numerical methods with the exception of polytropes with $n=0$
corresponding to the configurations with a uniform distribution of
energy density, when the solution is given in terms of elementary
functions. The geometry of the polytropes is conveniently represented by
embedding diagrams of both the ordinary space geometry and the optical
reference geometry reflecting some dynamical properties of the geodesic
motion. The polytropes are represented by radial profiles of energy
density, pressure, mass, and metric coefficients. For all tested values
of $n>0$, the static equilibrium configurations with fixed parameters
$n$, $sigma$, are allowed only up to a critical value of the
cosmological parameter
$lambda_{mathrm{c}}=lambda_{mathrm{c}}(n,sigma)$. In the case of
$n>3$, the critical value $lambda_{mathrm{c}}$ tends to zero for
special values of $sigma$. The gravitational potential energy and the
binding energy of the polytropes are determined and studied by numerical
methods. We discuss in detail the polytropes with an extension
comparable to those of the dark matter halos related to galaxies, i.e.,
with extension $ell > 100,mathrm{kpc}$ and mass $M >
10^{12},mathrm{M}_{odot}$. ...
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We show that the braneworld rotating Kerr-Newman black hole and naked
singularity spacetimes with both positive and negative braneworld tidal
charge parameters can be separated into 14 classes according to the
properties of circular geodesics governing the Keplerian accretion. We
determine the efficiency of the Keplerian accretion disks for all
braneworld Kerr-Newman spacetimes. We demonstrate the occurrence of an
infinitely deep gravitational potential in Kerr-Newman naked singularity
spacetimes having the braneworld dimensionless tidal charge b ∈(1 /4 ,1
) and the dimensionless spin a ∈(2 √{b }-√{b (4 b -1 ) } , 2 √{b }+√{b
(4 b -1 ) }) , implying unbound efficiency of the Keplerian accretion
and the possibility of extracting the whole naked singularity mass.
Therefore, we call them braneworld "mining-unstable" Kerr-Newman naked
singularity spacetimes. Fundamental restriction on the relevance of the
extraordinary—but fully classical—phenomenon of the mining instability
is given by validity of the assumption of geodesic motion of the
accreting matter.
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We show that the braneworld rotating Kerr-Newman black hole and naked
singularity spacetimes with both positive and negative braneworld tidal
charge parameters can be separated into 14 classes according to the
properties of circular geodesics governing the Keplerian accretion. We
determine the efficiency of the Keplerian accretion disks for all
braneworld Kerr-Newman spacetimes. We demonstrate the occurrence of an
infinitely deep gravitational potential in Kerr-Newman naked singularity
spacetimes having the braneworld dimensionless tidal charge b ∈(1
/4 ,1 ) and the dimensionless spin a ∈(2 √{b }-√{b (4 b
-1 ) } , 2 √{b }+√{b (4 b -1 ) }) , implying unbound
efficiency of the Keplerian accretion and the possibility of extracting
the whole naked singularity mass. Therefore, we call them braneworld
"mining-unstable" Kerr-Newman naked singularity spacetimes. Fundamental
restriction on the relevance of the extraordinary—but fully
classical—phenomenon of the mining instability is given by
validity of the assumption of geodesic motion of the accreting matter.
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We study motion and collision of particles in the gravitational field of
rotating black hole immersed in quintessential dark energy characterized
with the quintessential parameter ωqin(-1;-1/3) governing the
equation of state of the dark energy, and the dimensionless
quintessential field parameter tilde{c}. We focus on the acceleration of
particles due to collisional processes and show how the center of mass
energy depends on the quintessential field parameter tilde{c}. We also
make comparison of the obtained results to the collisional energetics of
quintessential static black holes demonstrating the crucial role of the
rotation parameter a in the particle acceleration. Finally we study the
dependence of the maximal value of the efficiency of energy extraction
through Penrose process for rotating black hole with quintessential
field parameter tilde{c}. It is found that quintessence field decreases
the energy extraction efficiency through Penrose process and when the
parameter tilde{c} vanishes one can get the standard value of the
efficiency coefficient for the Kerr black hole as η̃ 21 %.
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