Regular second order perturbations of binary black holes: The extreme mass ratio regime

TL;DR

This paper develops a second order perturbation framework for binary black holes in the extreme mass ratio regime, enabling precise gravitational waveform calculations for EMRIs, including regularization techniques and explicit waveform derivations.

Contribution

It introduces a regularized second order perturbation formulation in Schwarzschild spacetime, including explicit waveform calculations for head-on collisions, advancing the self-consistent radiation reaction analysis.

Findings

Effective source free of delta squares

Perturbations regular at particle location

Explicit second order waveforms for head-on collisions

Abstract

In order to derive the precise gravitational waveforms for extreme mass ratio inspirals (EMRI), we develop a formulation for the second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source build up from products of the first order perturbations and its derivatives. We have explicitly regularized this source at the horizon and at spatial infinity. We show that the effective source does not contain squares of the Dirac's delta and that perturbations are regular at the particle location. We introduce an asymptotically flat gauge for the radiation fields and the $\ell=0$ mode to compute explicitly the (leading) second order $\ell=2$ waveforms in the headon collision case. This case represents the first completion of the radiation reaction program self-consistently.