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

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, $a>0.99979$.

arXiv comment9 pages, 7 figures

References in corpus (1)

• Measuring mass and angular momentum of black holes with high-frequency quasi-periodic oscillations

Cited by in corpus (43)

• Circular orbits and related quasi-harmonic oscillatory motion of charged particles around weakly magnetized rotating black holes
• Appearance of Keplerian discs orbiting Kerr superspinars
• Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin
• Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
• Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows
• Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes
• General relativistic polytropes with a repulsive cosmological constant
• Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild-de Sitter spacetimes
• Mass of intermediate black hole in the source M82 X-1 restricted by models of twin high-frequency quasi-periodic oscillations
• LNRF-velocity hump-induced oscillations of a Keplerian disc orbiting near-extreme Kerr black hole: A possible explanation of high-frequency QPOs in GRS 1915+105
• Role of emission angular directionality in spin determination of accreting black holes with broad iron line
• Circular motion in NUT space-time
• Ringed accretion disks: evolution of double toroidal configurations
• Controversy of the GRO J1655-40 black hole mass and spin estimates and its possible solutions
• Humpy LNRF-velocity profiles in accretion discs orbiting nearly extreme Kerr black holes. A possible relation to QPOs
• Photon motion in Kerr-de Sitter spacetimes
• Relativistic thick accretion disks: morphology and evolutionary parameters
• Current-carrying string loops in black-hole spacetimes with a repulsive cosmological constant
• Observers in Kerr spacetimes: the ergoregion on the equatorial plane
• String loops oscillating in the field of Kerr black holes as a possible explanation of twin high-frequency quasiperiodic oscillations observed in microquasars
• Dynamical instability of polytropic spheres in spacetimes with a cosmological constant
• Geodesic Model of HF QPOs Tested for Black Holes in Spacetimes Reflecting the Effect of Surrounding Dark Matter
• Disclosing connections between black holes and naked singularities: Horizon remnants, Killing throats and bottlenecks
• Proto-jets configurations in RADs orbiting a Kerr SMBH: symmetries and limiting surfaces
• RADs energetics and constraints on emerging tori collisions around super-massive Kerr Black Holes
• Relating Kerr SMBHs in Active Galactic Nuclei to RAD configurations
• Mass estimate of the XTE J1650-500 black hole from the Extended Orbital Resonance Model for high-frequency QPOs
• Mass and Angular Momentum of Black Holes: An Overlooked Effect of General Relativity Applied to the Galactic Center Black Hole Sgr A*
• Nonlinear Einstein-Power-Yang-Mills AdS Black Holes: From Quantum Tunneling to Aschenbach Effect
• Non-monotonic orbital velocity profiles around rapidly rotating Kerr-(anti-)de Sitter black holes
• Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds
• Non-monotonic Keplerian velocity profiles around near-extreme braneworld Kerr black holes
• Aschenbach effect for spinning particles in Kerr spacetime
• Limiting effects in clusters of misaligned toroids orbiting static SMBHs
• Dragged surfaces. On the accretion tori in the ergoregion
• Jet collision with accreting tori around SMBHs. GRHD and light surfaces constraints in aggregates of misaligned tori
• Embedded BHs and multipole globules: Clustered misaligned thick accretion disks around static SMBHs
• Static spheres and Aschenbach effect for black holes in massive gravity
• Test of the string loop oscillation model using kHz quasiperiodic oscillations in a neutron star binary
• Aschenbach effect for spinning particles in Kerr-(A)dS spacetime
• On non-monotonic orbital velocity profiles around rapidly rotating Kerr-(anti)de Sitter black holes: acomment to the recently published results
• Extended orbital resonance model with hump-induced oscillations
• Multi-resonance orbital model applied to high-frequency quasi-periodic oscillations observed in Sgr A*