Transition from adiabatic inspiral to plunge into a spinning black hole

Understand

A test particle of mass mu on a bound geodesic of a Kerr black hole of mass M >> mu will slowly inspiral as gravitational radiation extracts energy and angular momentum from its orbit.

• This inspiral can be considered adiabatic when the orbital period is much shorter than the timescale on which energy is radiated, and quasi-circular when the radial velocity is much less than the azimuthal velocity.
• Although the inspiral always remains adiabatic provided mu << M, the quasi-circular approximation breaks down as the particle approaches the innermost stable circular orbit (ISCO).
• In this paper, we relax the quasi-circular approximation and solve the radial equation of motion explicitly near the ISCO.