A simple but powerful method how to visualize curved spacetimes is via
embedding diagrams of both ordinary geometry and optical reference
geometry 2D sections into 3D Euclidean space. They facilitate to gain an
intuitive insight into the gravitational field rendered into a curved
spacetime, and to assess the influence of spacetime metrics parameters.
Optical reference geometry and related inertial forces and their
relationship to embedding diagrams are particularly useful for
investigation of test particles motion. Embedding diagrams of static and
spherically symmetric, or stationary and axially symmetric black-hole
and naked-singularity space times thus present a useful concept for
intuitive understanding of these spacetimes' nature.
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Results of investigation of the behaviour of inertial forces related to
the optical reference geometry in the Kerr-de Sitter spacetimes and the
features of the embedding diagrams of the geometry are summarized.
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We developed realistic fully general relativistic computer code for
simulation of optical projection in a strong, spherically symmetric
gravitational field. Standard theoretical analysis of optical projection
for an observer in the vicinity of a Schwarzschild black hole is
extended to black hole spacetimes with a repulsive cosmological
constant, i.e, Schwarzschild-de Sitter (SdS) spacetimes. Influence of
the cosmological constant is investigated for static observers and
observers radially free-falling from static radius. Simulation includes
effects of gravitational lensing, multiple images, Doppler and
gravitational frequency shift, as well as the amplification of
intensity. The code generates images of static observers sky and a movie
simulations for radially free-falling observers. Techniques of parallel
programming are applied to get high performance and fast run of the
simulation code.
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Trapping of neutrinos in extremely compact stars containing trapped null
geodesics is studied. We calculated the ratio of produced to trapped
neutrinos in the simplest model of uniform density stars. This gives the
upper limit on trapping coefficients in real objects.
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The Sturm-Liouville eigenvalue equation for eigenmodes of the radial
oscillations is determined for spherically symmetric perfect fluid
configurations in spacetimes with a nonzero cosmological constant and
applied in the cases of 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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Basic properties of equipotential (equipressure) surfaces in test
barotropic perfect fluid tori with uniform distribution of the specific
angular momentum orbiting Kerr-de Sitter black holes are summarized. The
central mass-densities of adiabatic non-relativistic tori, for which the
approximation of test fluid is adequate, are given and compared with the
typical densities of Giant Molecular Clouds.
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Humpy LNRF-velocity profiles were found for both Keplerian thin discs
and marginally stable thick discs orbiting almost extreme Kerr black
holes, being located just above the innermost stable circular orbit. In
thick marginally stable discs, the global character of this phenomenon
is given by topology changes of equivelocity (von Zeipel) surfaces, as
the standard cylindrical von Zeipel surfaces are transformed into
toroidal surfaces existing around the circle corresponding to the local
minimum of the equatorial humpy LNRF-velocity profile. These phenomena
could indicate an instability in the disc triggering so-called "humpy"
oscillations, the frequency of which is estimated by the maximum
positive gradient of the humpy velocity profile in terms of the proper
radial distance. The humpy oscillations could force epicyclic
oscillations, if appropriate resonance conditions are satisfied.
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Fitting the observational data of the twin peak kHz quasiperiodic
oscillations (QPO) from low mass X-ray binaries (LMXBs) by the
relativistic precession model gives a substantially higher neutron star
mass estimate, M~2 Msolar, than the ``canonical value'', M~1.4 Msolar.
Using a fully general relativistic approach we discuss the non-geodesic
corrections to the orbital and epicyclic frequencies of slightly charged
circularly orbiting test particles caused by the presence of a neutron
star magnetic field. We show that consideration of such non-geodesic
corrections can bring down the neutron star mass estimate and improve
the quality of twin peak QPO data fits based on relativistic precession
frequency relations.
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A simple but powerful method how to visualize curved spacetimes is via embedding diagrams of both ordinary geometry and optical reference geometry 2D sections into 3D Euclidean space. They facilitate to gain an intuitive insight into the gravitational field rendered into a curved spacetime, and to assess the influence of spacetime metrics parameters. Optical reference geometry and related inertial forces and their relationship to embedding diagrams are particularly useful for investigation of test particles motion. Embedding diagrams of static and spherically symmetric, or stationary and axially symmetric black-hole and naked-singularity space times thus present a useful concept for intuitive understanding of these spacetimes' nature.
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