Photon capture cones and embedding diagrams of the Ernst spacetime

The differences between the character of the Schwarzschild and Ernst spacetimes are illustrated by comparing the photon capture cones, and the embedding diagrams of the $t=\mathrm{const}$ sections of the equatorial planes of both the ordinary and optical reference geometry of these spacetimes. The non-flat asymptotic character of the Ernst spacetime reflects itself in two manifest facts: the escape photon cones correspond to purely outward radial direction, and the embedding diagrams of both the ordinary and optical geometry shrink to zero radius asymptotically. Using the properties of the embedding diagrams, regions of these spacetimes which could have similar character are estimated, and it is argued that they can exist for the Ernst spacetimes with a sufficiently low strength of the magnetic field.Comment: 12 pages, 7 figure

Influence of the relict cosmological constant on accretion discs

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.Comment: 15 pages, 4 figures, invited pape

Humpy LNRF-velocity profiles in accretion discs orbiting nearly extreme Kerr black holes. A possible relation to QPOs

Change of sign of the LNRF-velocity gradient has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a > 0.9953 for Keplerian discs and a > 0.99979 for marginally stable thick discs. Aschenbach (2004) has identified the maximal rate of change of the orbital velocity within the "humpy" profile with a locally defined critical frequency of disc oscillations, but it has been done in a coordinate-dependent form. We define the critical "humpy" frequency H in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to distant observers. At radius of its definition, so-called "humpy" radius r_h, the "humpy" frequency H is compared to the radial (R) and vertical (V) epicyclic frequencies and the orbital frequency of the disc. For Keplerian thin discs, we show that the epicyclic resonance radii r_31 and r_41 (with V:R = 3:1 or 4:1) are located in vicinity of r_h where efficient triggering of oscillations with frequencies ~ H could be expected. Asymptotically (for 1-a < 10^(-4)) the ratio of the epicyclic and Keplerian frequencies and the humpy frequency is nearly constant, i.e., almost independent of spin, being for the radial epicyclic frequency R:H ~ 3:2. For thick discs the situation is more complex due to dependence on distribution of the specific angular momentum l determining the disc properties. For l = const tori and 1-a < 10^(-6) the frequency ratios of the humpy frequency and the orbital and epicyclic frequencies are again nearly constant and independent of both a and l, being for the radial epicyclic frequency R:H close to 4. In the limiting case of very slender tori (l ~ l_ms) the epicyclic resonance radius r_41 ~ r_h for spin 1-a < 2x10^(-4).Comment: 11 pages,10 figures, 1 table. Accepted for publication in Astronomy and Astrophysic

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).Comment: 6 pages, 4 figures, accepted by Astronomy & Astrophysic

Equatorial circular orbits in the Kerr-de Sitter spacetimes

Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin accretion discs is established.Comment: 24 pages, 19 figures, REVTeX

Centrifugally driven electrostatic instability in extragalactic jets

The stability problem of the rotation induced electrostatic wave in extragalactic jets is presented. Solving a set of equations describing dynamics of a relativistic plasma flow of AGN jets, an expression of the instability rate has been derived and analyzed for typical values of AGNs. The growth rate was studied versus the wave length and the inclination angle and it has been found that the instability process is much efficient with respect to the accretion disk evolution, indicating high efficiency of the instability.Comment: 7 pages, 4 figure

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius "RNS" is larger than the related radius of the marginally stable circular orbit "rms" for nuclear matter equations of state and spin frequencies up to 800Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius RNS is roughly equal to rms. The Paczynski modulation mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below one solar mass, and spin frequencies above 800Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.Comment: 7 pages, 4 figures (in colour), accepted for publication in Astronomy & Astrophysic

Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models

The strong gravitational field of neutron stars in the brany universe could be described by spherically symmetric solutions with a metric in the exterior to the brany stars being of the Reissner-Nordstrom type containing a brany tidal charge representing the tidal effect of the bulk spacetime onto the star structure. We investigate the role of the tidal charge in orbital models of high-frequency quasiperiodic oscillations (QPOs) observed in neutron star binary systems. We focus on the relativistic precession model. We give the radial profiles of frequencies of the Keplerian (vertical) and radial epicyclic oscillations. We show how the standard relativistic precession model modified by the tidal charge fits the observational data, giving estimates of the allowed values of the tidal charge and the brane tension based on the processes going in the vicinity of neutron stars. We compare the strong field regime restrictions with those given in the weak-field limit of solar system experiments.Comment: 26 pages, 6 figure