Isofrequency pairing of geodesic orbits in Kerr geometry

Abstract

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain "synchronized" in phase.

11 pages, 8 figures. Updated to reflect published version

References in corpus (10)

• X-ray Properties of Black-Hole Binaries
• Gravitational wave snapshots of generic extreme mass ratio inspirals
• A Periodic Table for Black Hole Orbits
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Verifying black hole orbits with gravitational spectroscopy
• Flare emission from Sagittarius A*
• The transition from adiabatic inspiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits

Cited by in corpus (35)

• Self-force and radiation reaction in general relativity
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Highly eccentric inspirals into a black hole
• Black hole perturbation theory and gravitational self-force
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• The location of the last stable orbit in Kerr spacetime
• Fast Self-forced Inspirals
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Importance of transient resonances in extreme-mass-ratio inspirals
• Resonantly enhanced and diminished strong-field gravitational-wave fluxes
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals
• The Astrophysics of Resonant Orbits in the Kerr Metric
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Fundamental frequencies and resonances from eccentric and precessing binary black hole inspirals
• Resonant self-force effects in extreme-mass-ratio binaries: A scalar model
• Adiabatic equatorial inspirals of a spinning body into a Kerr black hole
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Spin-orbit precession along eccentric orbits: improving the knowledge of self-force corrections and of their effective-one-body counterparts
• Ultralight scalars and resonances in black-hole physics
• Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?
• A Newtonian analogue of Kerr black hole
• A Note on Celestial Mechanics in Kerr Spacetime
• Analytic approximations, perturbation theory, effective field theory methods and their applications
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Transition of EMRIs through resonance: corrections to higher order in the on-resonance flux modification
• Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime
• A geometric origin for quasi-periodic oscillations in black hole X-ray binaries
• Isofrequency pairing of spinning particles in Schwarzschild-de Sitter spacetime
• MALBEC: a new CUDA-C ray-tracer in General Relativity
• Constants of motion in gravitational self-force theory
• KAM and geodesic dynamics of blackholes
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
• Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits