Test particle motion along equatorial circular orbits in the revisited Kerr-de Sitter spacetime

Both circular and epicyclic motion of test particles along equatorial circular orbits in the revisited Kerr-de Sitter spacetime is analyzed. We present relations for specific energy, specific angular momentum and Keplerian angular velocity of particles on equatorial circular orbits, and discuss criteria for the existence and stability of such orbits giving limits on spacetime parameters. Finally, we discuss the epicyclic motion along equatorial circular orbits obtaining relations for radial and vertical epicyclic frequencies. The results are compared with those for the standard Kerr-de Sitter geometry.Comment: 9 pages, 5 figures; to be published in Phys. Rev.

The Aschenbach effect: unexpected topology changes in motion of particles and fluids orbiting rapidly rotating Kerr black holes

Newton's theory predicts that the velocity $V$ of free test particles on circular orbits around a spherical gravity center is a decreasing function of the orbital radius $r$, $dV/dr < 0$. Only very recently, Aschenbach (A&A 425, p. 1075 (2004)) has shown that, unexpectedly, the same is not true for particles orbiting black holes: for Kerr black holes with the spin parameter $a>0.9953$, the velocity has a positive radial gradient for geodesic, stable, circular orbits in a small radial range close to the black hole horizon. We show here that the {\em Aschenbach effect} occurs also for non-geodesic circular orbits with constant specific angular momentum $\ell = \ell_0 = const$. In Newton's theory it is $V = \ell_0/R$, with $R$ being the cylindrical radius. The equivelocity surfaces coincide with the $R = const$ surfaces which, of course, are just co-axial cylinders. It was previously known that in the black hole case this simple topology changes because one of the ``cylinders'' self-crosses. We show here that the Aschenbach effect is connected to a second topology change that for the $\ell = const$ tori occurs only for very highly spinning black holes, $a>0.99979$.Comment: 9 pages, 7 figure

Role of electric charge in shaping equilibrium configurations of fluid tori encircling black holes

Astrophysical fluids may acquire non-zero electrical charge because of strong irradiation or charge separation in a magnetic field. In this case, electromagnetic and gravitational forces may act together and produce new equilibrium configurations, which are different from the uncharged ones. Following our previous studies of charged test particles and uncharged perfect fluid tori encircling compact objects, we introduce here a simple test model of a charged perfect fluid torus in strong gravitational and electromagnetic fields. In contrast to ideal magnetohydrodynamic models, we consider here the opposite limit of negligible conductivity, where the charges are tied completely to the moving matter. This is an extreme limiting case which can provide a useful reference against which to compare subsequent more complicated astrophysically-motivated calculations. To clearly demonstrate the features of our model, we construct three-dimensional axisymmetric charged toroidal configurations around Reissner-Nordstr\"om black holes and compare them with equivalent configurations of electrically neutral tori.Comment: 14 pages, 7 figure

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

Equatorial circular orbits in Kerr–Newman–de Sitter spacetimes

Circular motion of test particles in the equatorial plane of the Kerr–Newman–de Sitter (KNdS) spacetime is analyzed for both black-hole and naked-singularity backgrounds. We present relations for specific energy, specific angular momentum and Keplerian angular velocity of a particle on equatorial circular orbit, and discuss criteria for the existence of such orbits giving limits on spacetime parameters. The orientation of motion along circular orbits is discussed from the point of view of locally non-rotating frames. Finally, we discuss the stability of circular motion against radial perturbations and determine limits on the existence of stable circular orbits, as well as the structure of stability regions in KNdS spacetimes