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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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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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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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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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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Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant case of equilibrium positions in the equatorial plane of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes.
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The Swiss cheese model of the Universe with the superstring dark energy is constructed. The junction conditions are shown to be fulfilled and time evolution of the matching hypersurface of the internal Schwarzschild spacetime and homogeneous external Friedman Universe is studied.
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The Friedman models of the Universe with the superstring dark energy are constructed. According to the spacetime foam approach the stringy dark energy appears to be inversely proportional to the cosmic scale factor. Evolution of the Friedman models is discussed under this assumption and compared with the standard models.
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The equation governing small radial oscillations and the related Sturm-Liouville eigenvalue equation for eigenmodes of the oscillations are determined for spherically symmetric configurations of perfect fluid in spacetimes with a nonzero cosmological constant. The Sturm-Liouville equation is then applied in the cases of spherically symmetric configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.
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