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Newton's theory predicts that the velocity $V$ of free test particles oncircular orbits around a spherical gravity center is a decreasing function ofthe 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 forparticles 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. Weshow here that the {\em Aschenbach effect} occurs also for non-geodesiccircular orbits with constant specific angular momentum $\ell = \ell_0 =const$. In Newton's theory it is $V = \ell_0/R$, with $R$ being the cylindricalradius. The equivelocity surfaces coincide with the $R = const$ surfaces which,of course, are just co-axial cylinders. It was previously known that in theblack hole case this simple topology changes because one of the ``cylinders''self-crosses. We show here that the Aschenbach effect is connected to a secondtopology change that for the $\ell = const$ tori occurs only for very highlyspinning black holes, $a>0.99979$.Comment: 9 pages, 7 figure

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