Aschenbach effect: Unexpected topology changes in the motion of particles and fluids orbiting rapidly rotating Kerr black holes
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 blackhole horizon. We show here that the Aschenbach effect occurs also for nongeodesic circular orbits with constant specific angular momentum ℓ=ℓ_{0}=const. In Newtonian theory it is V=ℓ_{0}/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 blackhole case this simple topology changes because one of the “cylinders” selfcrosses. 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.
 Publication:

Physical Review D
 Pub Date:
 January 2005
 DOI:
 10.1103/PhysRevD.71.024037
 arXiv:
 arXiv:grqc/0411091
 Bibcode:
 2005PhRvD..71b4037S
 Keywords:

 04.20.Gz;
 04.70.s;
 95.30.Sf;
 Spacetime topology causal structure spinor structure;
 Physics of black holes;
 Relativity and gravitation;
 General Relativity and Quantum Cosmology
 EPrint:
 9 pages, 7 figures