The centrifugal force reversal and X-ray bursts

Heyl (2000) made an interesting suggestion that the observed shifts in QPO frequency in type I X-ray bursts could be influenced by the same geometrical effect of strong gravity as the one that causes centrifugal force reversal discovered by Abramowicz and Lasota (1974). However, his main result contains a sign error. Here we derive the correct formula and conclude that constraints on the M(R) relation for neutron stars deduced from the rotational-modulation model of QPO frequency shifts are of no practical interest because the correct formula implies a weak condition R* > 1.3 Rs, where Rs is the Schwarzschild radius. We also argue against the relevance of the rotational-modulation model to the observed frequency modulations.Comment: 3 pages, Minor revisions, A&A Letters, in pres

The proton and the photon, who is probing whom in electroproduction?

The latest results on the structure of the proton and the photon as seen at HERA are reviewed while discussing the question posed in the title of the talk.Comment: 18 pages, including 28 figures. To be published in the proceedings of the 2nd KEK-Tanashi International Symposium on Hadron and Nuclear Physics with Electromagnetic Probes, KEK-Tanashi, Tokyo, Japan, October 25-27, 1999. Typos in eqs (8) and (9) corrected and reference 5 update

The statistics of Sco X-1 kHZ QPOs

Recently an additional technique was applied to investigate the properties of kHz QPOS, i.e. the analysis of the distribution of frequency ratios or frequencies themselves. I review the results of such work on the data from ScoX-1: Abramowicz et al. (2003), which was later criticized by Belloni et al.(2005). I conclude that the findings of the latter paper are consistent with results presented earlier: kHz QPOs cluster around the value corresponding to the frequency ratio of 2/3. I also discuss the random walk model of kHz QPOs and possible future observations needed to verify it.Comment: Astronomische Nachrichten, in pres

On the Polish doughnut accretion disk via the effective potential approach

We revisit the Polish doughnut model of accretion disks providing a comprehensive analytical description of the Polish doughnut structure. We describe a perfect fluid circularly orbiting around a Schwarzschild black hole, source of the gravitational field, by the effective potential approach for the exact gravitational and centrifugal effects. This analysis leads to a detailed, analytical description of the accretion disk, its toroidal surface, the thickness, the distance from the source. We determine the variation of these features with the effective potential and the fluid angular momentum. Many analytical formulas are given. In particular it turns out that the distance from the source of the inner surface of the torus increases with increasing fluid angular momentum but decreases with increasing energy function defined as the value of the effective potential for that momentum. The location of torus maximum thickness moves towards the external regions of the surface with increasing angular momentum, until it reaches a maximum an then decreases. Assuming a polytropic equation of state we investigate some specific cases.Comment: 33 pages, 28 figures, 1 table. This is a revised version to meet the published articl

An intuitive approach to inertial forces and the centrifugal force paradox in general relativity

As the velocity of a rocket in a circular orbit near a black hole increases, the outwardly directed rocket thrust must increase to keep the rocket in its orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we show that it follows naturally from the equivalence principle together with special relativity and a few general features of black holes. We also derive a general relativistic formalism of inertial forces for reference frames with acceleration and rotation. The resulting equation relates the real experienced forces to the time derivative of the speed and the spatial curvature of the particle trajectory relative to the reference frame. We show that an observer who follows the path taken by a free (geodesic) photon will experience a force perpendicular to the direction of motion that is independent of the observers velocity. We apply our approach to resolve the submarine paradox, which regards whether a submerged submarine in a balanced state of rest will sink or float when given a horizontal velocity if we take relativistic effects into account. We extend earlier treatments of this topic to include spherical oceans and show that for the case of the Earth the submarine floats upward if we take the curvature of the ocean into account.Comment: 14 pages, 21 figure