It is highly probable that a non-linear resonance between some modes of oscillations in the accretion discs around black holes and neutron stars can play a crucial role in exciting detectable modulations of the X-ray flux. Detailed studies of the resonance models revealed that several of such non-linear resonances are possible in nearly Keplerian discs in strong gravity. Moreover, this idea seems to be strongly supported by observations - in all four microquasars showing twin peak QPOs (quasiperiodic oscillations), the ratio of frequency peaks is 3:2. In principle, using known frequencies of the twin peaks and the known mass of the central black hole, the black-hole spin can be determined. This was already done for the presently known sources and few miscellaneous resonance models. Details of excitation mechanisms of eventual resonances are still not fully explained, nevertheless one can imagine that not only one resonance could be excited in the accretion disc. Thus, if two such different resonances are present (by an accident or because of some causal connection), the black hole spin can be precisely determined independently of the knowledge of the black hole mass, for some specific cases discussed here.
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Extremely compact objects (R<3 GM/c2) contain null geodesics that are captured by the object. Certain part of neutrinos produced in their interior will therefore be trapped, thus influencing neutrino luminosity of the objects and their thermal evolution. This effect was investigated for the interior Schwarzschild spacetimes with the uniform distribution of energy density by Stuchlík, Z., Török, G., Hledík, S. and Urbanec, M. (2005), Neutrino trapping in extremely compact objects, Classical Quantum Gravity, submitted. We will investigate here influence of the cosmological constant on the trapping phenomena. We use again the simplest model for interior of such objects based on the interior Schwarzschild-(anti-)de Sitter spacetimes. We determine behaviour of the trapping coefficients, i.e., ``global'' one representing influence on the neutrino luminosity and ``local'' one representing influence on the cooling process.
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Relativistic Keplerian orbital frequency (νK) and the related epicyclic frequencies (radial νr, vertical νθ) play an important role in the physics of accretion discs orbiting Kerr black holes. We examine in detail their properties in Kerr spacetimes and discuss some possible observational implications resulting from their behaviour in the black hole case. Characteristics of the fundamental orbital frequencies of Keplerian motion are also analysed with the intention to find the phenomena which could observationally distinguish a hypothetical naked singularity from black holes. We explore the significant differences in behaviour of the epicyclic frequencies. These suggest that oscillations of discs orbiting Kerr black holes and naked singularities could be very different, and the information, given through X-ray variability of the source, could distinguish between the naked singularities and the black holes in general.
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The discussion of the latitudinal and radial photon motion in the Kerr- de Sitter (KdS) spacetime is examined by using the ``Chinese boxes'' technique. Only the case with a positive cosmological constant is considered. The latitudinal motion is discussed by using a new motion constant Q vanishing for motion in the equatorial plane. This will be more comfortable for the next discussion of the photon off-equatorial motion in KdS spacetime. For the radial motion an ``effective potential'' governing the photon radial motion is used, circular photon orbits are determined and their stability is discussed.
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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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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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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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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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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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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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