Binary black hole merger in the extreme-mass-ratio limit

We discuss the transition from quasi-circular inspiral to plunge of a system of two nonrotating black holes of masses m1 and m2 in the extreme-mass-ratio limit m1m2 /(m1 + m2)^2. In the spirit of the effective one body (EOB) approach to the general relativistic dynamics of binary systems, the dynamics of the two black hole system is represented in terms of an effective particle of mass μ ≡ m1m2/(m1 +m2) moving in a (quasi-)Schwarzschild background of mass M ≡ m1 + m2 and submitted to an O(μ) radiation reaction force defined by Pad´e resumming high-order post-Newtonian results. We then complete this approach by numerically computing, in the style of Regge–Wheeler–Zerilli, the gravitational radiation emitted by such a particle. Several tests of the numerical procedure are presented. We focus on gravitational waveforms and the related energy and angular momentum losses. We view this work as a contribution to the matching between analytical and numerical methods within an EOB-type framework.