**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.;