Near a black hole or an ultracompact star, the motion of particles is
governed by a strong gravitational field. Electrically charged particles
also feel the electromagnetic force arising due to currents inside the
star or plasma circling around. We study the possibility that the
interplay between gravitational and electromagnetic actions may allow
for the stable, energetically bound off-equatorial motion of charged
particles. This would represent the well-known generalized
Störmer's 'halo orbits', which have been discussed in connection
with the motion of dust grains in planetary magnetospheres. We
demonstrate that such orbits exist and can be astrophysically relevant
when a compact star or a black hole is endowed with a dipole-type
magnetic field. In the case of the Kerr Newman solution, numerical
analysis shows that the mutually connected gravitational and
electromagnetic fields do not allow the existence of stable halo orbits
above the outer horizon of black holes. Such orbits are either hidden
under the inner black-hole horizon, or they require the presence of a
naked singularity.
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The equations of state (EoS) of relativistic asymmetric nuclear matter
are obtainable from assumed form of the interaction Lagrangian. They are
one of important inputs to describe the neutron stars. The structure of
the neutron stars, i.e. the density of matter and the pressure as
functions of radial distance starting from their values at the center of
a star, is straightforwardly dependent on EoS. Similarly, a limitation
on the total mass of the neutron star can be obtained therefrom. Thus,
EoS and the underlying nucleon interactions can be tested also by the
means of astronomical observations.
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Near a black hole or an ultracompact star, the motion of particles is governed by a strong gravitational field. Electrically charged particles also feel the electromagnetic force arising due to currents inside the star or plasma circling around. We study the possibility that the interplay between gravitational and electromagnetic actions may allow for the stable, energetically bound off-equatorial motion of charged particles. This would represent the well-known generalized Störmer's 'halo orbits', which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of the Kerr Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow the existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.
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The equations of state (EoS) of relativistic asymmetric nuclear matter are obtainable from assumed form of the interaction Lagrangian. They are one of important inputs to describe the neutron stars. The structure of the neutron stars, i.e. the density of matter and the pressure as functions of radial distance starting from their values at the center of a star, is straightforwardly dependent on EoS. Similarly, a limitation on the total mass of the neutron star can be obtained therefrom. Thus, EoS and the underlying nucleon interactions can be tested also by the means of astronomical observations.
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Properties of the Reissner-Nordstr"om black-hole and naked-singularity
spacetimes with a nonzero cosmological constant are represented by their
geodetical structure and embedding diagrams of the central planes of
both the ordinary geometry and associated optical reference geometry.
Motion of test particles and photons is described in terms of an
appropriate `effective potential.' Circular geodesics are discussed and
photon escape cones are determined. In all asymptotically anti-dS
black-hole spacetimes and some asymptotically dS black-hole spacetimes a
region containing stable circular geodesics exists, which allows
accretion processes in the disk regime. The inner region is limited from
below by particles with zero angular momentum that are located in stable
equilibrium positions. The inertial and gravitational forces related to
the optical reference geometry are introduced and specified for the
circular motion. It is shown how the properties of the centrifugal force
are closely related to the properties of the optical reference geometry
embedding diagrams.
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Interior solutions of Einstein's equations with a non-zero cosmological
constant are given for static and spherically symmetric configurations
of uniform density. The metric tensor and pressure are determined for
both positive and negative values of the cosmological constant. Limits
on the outer radius of the interior solutions are established. It is
shown that, contrary to the cases of the limits on the interior
Schwarzschild and Reissner--Nordstr"om solutions with a zero
cosmological constant, these limits do not fully coincide with the
conditions of embeddability of the optical reference geometry associated
with the exterior (vacuum) Schwarzschild--de Sitter spacetime.
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A recently published study on long term evolution of the frequencies of
the kilohertz quasi-periodic oscillations (QPOs) in the atoll source 4U
1636-53 concluded that there is no preferred frequency ratio in a
distribution of twin QPOs that was inferred from the distribution of a
single frequency alone. However, we find that the distribution of the
ratio of actually observed pairs of kHz QPO frequencies is peaked close
to the 3/2 value, and possibly also close to the 5/4 ratio. To resolve
the apparent contradiction between the two studies, we examine in detail
the frequency distributions of the lower kHz QPO and the upper kHz QPO
detected in our data set. We demonstrate that for each of the two kHz
QPOs (the lower or the upper), the frequency distribution in all
detections of a QPO differs from the distribution of frequency of the
same QPO in the subset of observations where both the kHz QPOs are
detected. We conclude that detections of individual QPOs alone should
not be used for calculation of the distribution of the frequency ratios.
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Relation between the lower and upper frequency mode of the twin peak
quasi-periodic oscillations observed in the neutron star X-ray binaries
is qualitatively well fitted by the frequency relation following from
the relativistic precession model. Assuming this model with no preferred
radius and the probability of an observable twin QPO excitation being
uniform across the inner edge of an accretion disk we compare the
expected and observed twin peak QPO distribution in the case of atoll
source 4U 1636-53. We find these two distributions highly incompatible.
We argue that the observed distribution roughly corresponds to the
expected one if an additional consideration of preferred resonant orbits
is included. We notice that our findings are relevant for some
disk-oscillation QPO models as well.
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Properties of the Reissner-Nordström black-hole and naked-singularity spacetimes with a nonzero cosmological constant are represented by their geodetical structure and embedding diagrams of the central planes of both the ordinary geometry and associated optical reference geometry. Motion of test particles and photons is described in terms of an appropriate `effective potential.' Circular geodesics are discussed and photon escape cones are determined. In all asymptotically anti-dS black-hole spacetimes and some asymptotically dS black-hole spacetimes a region containing stable circular geodesics exists, which allows accretion processes in the disk regime. The inner region is limited from below by particles with zero angular momentum that are located in stable equilibrium positions. The inertial and gravitational forces related to the optical reference geometry are introduced and specified for the circular motion. It is shown how the properties of the centrifugal force are closely related to the properties of the optical reference geometry embedding diagrams.
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Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative values of the cosmological constant. Limits on the outer radius of the interior solutions are established. It is shown that, contrary to the cases of the limits on the interior Schwarzschild and Reissner--Nordström solutions with a zero cosmological constant, these limits do not fully coincide with the conditions of embeddability of the optical reference geometry associated with the exterior (vacuum) Schwarzschild--de Sitter spacetime.
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