Self-consistent adiabatic inspiral and transition motion

Abstract

The transition motion of a point particle around the last stable orbit of Kerr is described at leading order in the transition-timescale expansion. Taking systematically into account all self-force effects, we prove that the transition motion is still described by the Painlevé transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasi-circular adiabatic inspiral with the transition motion. The matching requires us to take into account the secular change of angular velocity due to radiation reaction during the adiabatic inspiral.

Matches the Erratum version in Physical Review Letters, 6 pages

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• Transition-to-plunge self-force waveforms with a spinning primary
• Success of the small mass ratio approximation during the final orbits of binary black hole simulations
• Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset
• Asymptotically matched quasi-circular inspiral and transition-to-plunge in the small mass ratio expansion
• Redshift factor and the small mass-ratio limit in binary black hole simulations
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane