Transition from adiabatic inspiral to plunge into a spinning black hole

TL;DR

This paper analyzes the transition from adiabatic inspiral to plunge into a Kerr black hole, explicitly solving the radial motion near the ISCO to improve predictions of black hole spin and mass changes after mergers.

Contribution

It introduces a new method to calculate the energy-angular momentum difference during the transition, improving predictions for black hole spin evolution in mergers.

Findings

Explicit solution of radial motion near ISCO

New contribution to energy-angular momentum difference

Implications for black hole spin and mass predictions

Abstract

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. We use the requirement that the test particle's 4-velocity remain properly normalized to calculate a new contribution to the difference between its energy and angular momentum. This difference determines how a black hole's spin changes following a test-particle merger, and can be extrapolated to help predict the mass and spin of the final black hole produced in finite-mass-ratio black-hole mergers. Our new contribution is particularly important for nearly maximally spinning black holes, as it can affect whether a merger produces a naked singularity.