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

TL;DR

The paper investigates the Aschenbach effect, revealing unexpected topology changes in particle and fluid motion around rapidly rotating Kerr black holes, especially for near-extremal spins exceeding 0.99979.

Contribution

It demonstrates that the Aschenbach effect occurs for non-geodesic circular orbits with constant angular momentum and links it to a second topology change in the orbital structure for very high black hole spins.

Findings

Aschenbach effect occurs for non-geodesic orbits with constant angular momentum.

Topology change in equivelocity surfaces linked to high black hole spins.

Effect appears only for black holes with spin parameter greater than 0.99979.

Abstract

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, $a>0.99979$.