Newtons 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 Newtons 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, $a>0.99979$.
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