Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black hole and naked-singularity space-times with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being nonzero. The space-times are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish.
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Change of sign of the velocity gradient (mesured with respect to locally non-rotating frames) has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a > 0.9953 for Keplerian discs [1] and a > 0.99979 for marginally stable thick discs [2]. Such "humpy" orbital velocity profiles occur close to but above the marginally stable circular geodesic of the black hole spacetimes. The maximal positive rate of change of the orbital velocity in terms of the proper radial distance introduces a locally defined critical frequency characterizing any processes in the disc capable to excite possible oscillations connected with the velocity hump. Comparing the "humpy frequency" related to distant observers with the epicyclic frequencies we show that in Keplerian discs orbiting extremely rapid Kerr holes (1 - a < 10-4 ) the ratio of the epicyclic frequencies and the humpy frequency is nearly constant, i.e., almost independent of a, being ∼ 3 : 2 for the radial epicyclic frequency and ∼ 11 : 2 for the vertical epicyclic frequency. For black holes with a ∼ 0.996, i.e., when the resonant phenomena with ratio 3 : 1 between the vertical and radial epicyclic oscillations occur near the radius of the critical humpy frequency, the ratio of the radial epicyclic and the humpy frequency is ∼ 12 : 1, which is close to the ratio between high- and low- frequency QPO in X-ray systems. For a > 0.996 the resonant orbit r4:1 (with the ratio 4 : 1 between the vertical and radial epicyclic oscillations) occurs in the region of the hump. Applying the model on the nearly extreme black hole candidate GRS 1915+105, we conclude that for black hole parameters M = 14.8M⊙ and a = 0.9998 the observed high-frequency QPOs could be related to the hump-induced oscillations in thin accretion disc, as the first two QPOs, 41 Hz and 67 Hz, can be identified with the "humpy frequency" and the radial epicyclic frequency (at the same orbit). The other observed QPO-frequencies, 113 Hz and 166 Hz, can be explained as the combinational ones of the "humpy" and epicyclic frequencies.
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Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray bi- naries. It has been suggested that the kHz QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting disk oscillations. A 3:2 resonant ratio of frequencies has been clearly recognized in the black-hole QPO data supporting the non-linear resonance hypothesis. It is often discussed whether the same 3:2 ratio appears in case of the neutron star QPOs as well. For an individual neutron star source, the relation between the observed lower and upper (νL and νU ) kHz QPO frequency is well approximated by a linear relation with the slope A and the shift B, i.e., νU = AνL + B. It was recognized only recently that for a group of twelve neutron star sources the value of the individual coefficients A, B is anticorre- lated, obeying the condition A = 3/2 - 0.0016B. It was also shown that such an anticorrelation is predicted by the theory of weakly coupled nonlinear oscillators, and one can argue that it indeed pose the evidence for a 3:2 resonant ratio. Here, stressing the latest progress, we discuss some of the links between the QPO observation and the resonance model, and summarize the appropriate references. Except the slightly updated list of references, the content of next four pages fully correspond to the A0 poster we exhibited at the VI Microquasar Workshop. The poster itself is available at the http://www.physics.cz/research (section Conferences).
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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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