Publication date: Jan 2005
Abstract:
Newtonian 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 [B. Aschenbach, Astronomy and Astrophysics, 425, 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 Aschenbach effect occurs also for
nongeodesic circular orbits with constant specific angular momentum
ℓ=ℓ0=const. In Newtonian theory it is V=ℓ0/R, with
R being the cylindrical radius. The equivelocity surfaces coincide with
the R=const surfaces which, of course, are just coaxial cylinders. It
was previously known that in the black-hole case this simple topology
changes because one of the “cylinders” self-crosses. The results
indicate that the Aschenbach effect is connected to a second topology
change that for the ℓ=const tori occurs only for very highly spinning
black holes, a>0.99979.
Authors:
Stuchlík, Zdeněk; Slaný, Petr; Török, Gabriel; Abramowicz, Marek A.;