Binary black hole merger in the extreme mass ratio limit

TL;DR

This paper models the transition from inspiral to plunge in extreme mass ratio black hole mergers using an Effective One Body approach, combining analytical and numerical methods to compute gravitational waveforms and energy losses.

Contribution

It introduces a novel EOB-based framework for extreme mass ratio mergers, integrating high-order Post-Newtonian results with numerical gravitational wave calculations.

Findings

Validated numerical methods for gravitational wave emission

Produced gravitational waveforms and energy loss estimates

Enhanced understanding of inspiral-plunge transition in extreme mass ratios

Abstract

We discuss the transition from quasi-circular inspiral to plunge of a system of two nonrotating black holes of masses $m_1$ and $m_2$ in the extreme mass ratio limit $m_1m_2\ll (m_1+m_2)^2$. 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 $\mu\equiv m_1m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M\equiv m_1+m_2$ and submitted to an ${\cal O}(\mu)$ radiation reaction force defined by Pad\'e resumming high-order Post-Newtonian results. We then complete this approach by numerically computing, \`a la 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.