W. Kluzniak

Epicyclic oscillations of fluid bodies: II. Strong gravity

Fluids in external gravity may oscillate with frequencies characteristic of the epicyclic motions of test particles. We explicitly demonstrate that global oscillations of a slender, perfect fluid torus around a Kerr black hole admit incompressible vertical and radial epicyclic modes. Our results may be directly relevant to one of the most puzzling astrophysical phenomena—high (hundreds of hertz) frequency quasiperiodic oscillations (QPOs) detected in x-ray fluxes from several black hole sources. Such QPOs are pairs of stable frequencies in the 3/2 ratio. It seems that they originate a few gravitational radii away from the black hole and thus their observations have the potential to become an accurate probe of super-strong gravity.

Spinning up black holes with super-critical accretion flows

We study the process of spinning up black holes by accretion from slim disks in a wide range of accretion rates. We show that for super-Eddington accretion rates and low values of the viscosity parameter � (. 0.01) the limiting value of the dimensionless spin parameter a∗ can reach values higher than a∗ = 0.9978 inferred by Thorne (1974) in his seminal study. For u M = 10 u MEdd and � = 0.01 spin equilibrium is reached at a∗ = 0.9994. We show that the equilibrium spin value depends strongly on the assumed value of �. We also prove that for high accretion rates the impact of captured radiation on spin evolution is negligible.

Holonomy invariance, orbital resonances and kilohertz QPOs

Quantized orbital structures are typical for many aspects of classical gravity (Newtons as well as Einsteins). The astronomical phenomenon of orbital resonances is a well-known example. Recently, Rothman et al (2001 Class. Quantum Grav. 18 1217–33) discussed quantized orbital structures in the novel context of a holonomy invariance of parallel transport in Schwarzschild geometry. We present here yet another example of quantization of orbits, one that is closely related to orbital resonances and closely analogous to holonomy invariance. This strong-gravity effect may have been already directly observed as the puzzling kilohertz quasi-periodic oscillations (QPOs) in the x-ray emission from a few accreting galactic black holes and several neutron stars.

Twin paradox on the photon sphere

We consider a new version of the twin paradox. The twins move along the same circular free photon path around the Schwarzschild center. In this case, despite their different velocities, all twins have the same non-zero acceleration. On the circular photon path, the symmetry between the twins situations is broken not by acceleration (as it is in the case of the classic twin paradox), but by the existence of an absolute standard of rest (timelike Killing vector). The twin with the higher velocity with respect to the standard of rest is younger on reunion. This closely resembles the case of periodic motions in compact (non-trivial topology) 3-D space recently considered in the context of the twin paradox by Barrow and Levin, except that there accelerations of all twins were equal to zero, and that in the case considered here, the 3-D space has trivial topology.

Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes

The sum of squared epicyclic frequencies of nearly circular motion (omega^(2)_(r) + omega^(2)_(theta)) in axially symmetric configurations of Newtonian gravity is known to depend both on the matter density and on the angular velocity profile of circular orbits. It was recently found that this sum goes to zero at the photon orbits of Schwarzschild and Kerr spacetimes. However, these are the only relativistic configurations for which such a result exists in the literature. Here, we extend the above formalism in order to describe the analogous relation for geodesic motion in arbitrary static, axially symmetric, asymptotically flat solutions of general relativity. The sum of squared epicyclic frequencies is found to vanish at photon radii of vacuum solutions. In the presence of matter, we obtain that omega^(2)_(r) + omega^(2)_(theta) > 0 for perturbed timelike circular geodesics on the equatorial plane if the strong energy condition holds for the matter-energy fluid of spacetime; in vacuum, the allowed region for timelike circular geodesic motion is characterized by the inequality above. The results presented here may be of use to shed light on general issues concerning the stability of circular orbits once they approach photon radii, mainly the ones corresponding to stable photon motion.