Self-consistent adiabatic inspiral and transition motion

TL;DR

This paper models the transition motion of a particle near a Kerr black hole's last stable orbit, incorporating self-force effects and matching adiabatic inspiral with transition dynamics using asymptotic expansions.

Contribution

It provides a self-consistent description of transition motion including all self-force effects and matches it with adiabatic inspiral using asymptotic methods.

Findings

Transition motion described by Painlevé transcendent equation.

Consistent matching of inspiral and transition phases achieved.

Secular change in angular velocity due to radiation reaction incorporated.

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 Painlev\'e 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.