Properties of the gravitational perturbation force caused by a small inhomogeneity located on the surface of a neutron star are studied. The oscillating perturbation force in both the accretion disc rotating around the star and in the interior of a differentially rotating star is determined. Both vertical and radial components of the force are given and their relations are discussed. The frequency of the oscillations is given by the difference of the frequency of the rotation of the star surface, and the orbital frequency in the disc (the frequency of rotation of matter in the star interior). Outside the star, in the disc, the vertical and radial forces vary with the same phase. Inside a differentially rotating star, the variations of the forces are in the opposite phase in an internal part of the star, while they are in the same phase in an external layer of the star. In an intermediate part of the star, an additional oscillatory change appears. Is is shown that the anharmonic character of the oscillatory forces is limited to the seventh non-negligible harmonics. For completeness, we present the perturbation force generated by a symmetric accretion column.
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Perfect fluid tori with uniform distribution of the specific angular momentum, l(r θ)= const, orbiting the Kerr-de Sitter naked singularities are discussed. Closed equipotential surfaces corresponding to stationary thick discs are allowed only in the spacetimes admitting stable circular geodesics. The last closed surface crosses itself in the cusp(s) enabling outflows of matter from the torus due to the violation of hydrostatic equilibrium. The inner cusp enables the accretion onto the ring singularity. Influence of the repulsive cosmological constant, Λ > 0, resides in the existence of the outer cusp enabling the excretion (outflow of matter from the torus into the outer space) and gives rise to completely new type of a disc called the excretion disc. The plus-family accretion and excretion discs can be both the corotating or counterrotating discs, the minus-family ones are always the counterrotating discs, as related to locally non-rotating frames. If the parameters of naked-singularity spacetimes are very close to the parameters of the extreme black-hole spacetimes, the family of possible disc-like configurations includes members with two isolated discs where the inner one is always a counterrotating accretion disc, while the outer one can be the corotating or counterrotating excretion disc, as well as the counterrotating accretion disc.
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We examine halo orbits of electrically charged particles near a magnetized compact star. We compare the Newtonian and Pseudo-Newtonian approaches to the Störmer problem as a preliminary discussion of the full general relativistic approach. We show the differences in the effective potential that arise due to strong gravity near a gravitating body.
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The integrals of photon motion in the Kerr spacetimes are given in terms of the emission angles related to emitters moving along the circular geodesic orbits. The local frames of the circular geodesic emitters are given in relation to the locally nonrotating frames and local directional angles of the escape cones are given in terms of the motion constants of photons.
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Equilibrium configurations that are solutions of spherically symmetric hydrostatic equations of General Relativity for an ideal fluid obeying a polytropic (or adiabatic) equation of state are given in the framework of general relativity. The equilibrium configurations are given in terms of the polytropic index n and the so called relativistic parameter σ (for polytropes) or α (for adiabates). First, simple models of polytropic and adiabatic spheres for non-relativistic and ultra-relativistic case of the equation of state are introduced. Then, the comparison of polytropic and adiabatic spheres is given in some special characteristic cases and the influence of the relativistic parameter on the structure of the spheres and the gravitational and binding energy.
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Embedding diagrams of the equatorial plane of the Kerr-de Sitter black-hole or naked-singularity spacetimes are constructed for the optical reference geometry. The embedding diagrams do not cover whole stationary parts of the Kerr-de Sitter spacetimes. Hence, limits of embeddability are discussed. The Kerr-de Sitter spacetimes are then classified according to the number of embeddable regions and the number of the turning points of the diagrams.
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We describe a new method to developing a realistic fully general relativistic model and computer code of optical projection in a strong, spherically symmetric gravitational field. Classical theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole was extended to black hole spacetimes with a repulsive cosmological constant (Schwarzschild-de Sitter spacetimes). In our simulation we consider both null geodesics beyond and ahead of the turning point. Simulation takes care of frequency shift effects, as well as the amplification of intensity. Our code generates static images of sky for static observers and movie simulation for free-falling observers. We use techniques of parallel programming to get high performance and fast run of our code.
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In this Proceedings, the talks presented during workshops RAGtime 6/7: Workshops on black holes and neutron stars, Opava, 16-18/18-20 September 2004/2005 are collected.
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Surprisingly, the relict cosmological constant has a crucial influence
on properties of accretion discs orbiting black holes in quasars and
active galactic nuclei. We show it by considering basic properties of
both the geometrically thin and thick accretion discs in the Kerr-de
Sitter black hole (naked-singularity) spacetimes. Both thin and thick
discs must have an outer edge allowing outflow of matter into the outer
space, located nearby the so-called static radius, where the
gravitational attraction of a black hole is balanced by the cosmological
repulsion. Jets produced by thick discs can be significantly collimated
after crossing the static radius. Extension of discs in quasars is
comparable with extension of the associated galaxies, indicating a
possibility that the relict cosmological constant puts an upper limit on
extension of galaxies.
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Perfect fluid tori with a uniform distribution of the specific angular
momentum, ell(r, θ) = const, orbiting the Kerr de Sitter black
holes or naked singularities are studied. It is well known that the
structure of equipotential surfaces of such marginally stable tori
reflects the basic properties of any tori with a general distribution of
the specific angular momentum. Closed equipotential surfaces
corresponding to stationary thick discs are allowed only in the
spacetimes admitting stable circular geodesics. The last closed surface
crosses itself in the cusp(s) enabling the outflow of matter from the
torus due to the violation of hydrostatic equilibrium. The inner cusp
enables an accretion onto the central object. The influence of the
repulsive cosmological constant, Λ > 0, on the equipotential
surfaces lies in the existence of the outer cusp (with a stabilizing
effect on the thick discs) and in the strong collimation of open
equipotential surfaces along the rotational axis. Both the effects take
place near a so-called static radius where the gravitational attraction
is just balanced by the cosmic repulsion. The outer cusp enables
excretion, i.e., the outflow of matter from the torus into the outer
space. The plus-family discs (which are always co-rotating in the
black-hole backgrounds but can be counter-rotating, even with negative
energy of the fluid elements, in some naked-singularity backgrounds) are
thicker and more extended than the minus-family ones (which are always
counter-rotating in all backgrounds). For co-rotating discs in the
naked-singularity spacetimes, the potential well between the centre of
the disc and its edges at the cusps is usually much higher than in the
black-hole spacetimes. If the parameters of naked-singularity spacetimes
are very close to the parameters of extreme black-hole spacetimes, the
family of possible disc-like configurations includes members with two
isolated discs where the inner one is always a counter-rotating
accretion disc.
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