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 ℓ = 0 mode to compute explicitly the (leading) second order ℓ = 2 waveforms in the headon collision case. This case represents the first completion of the radiation reaction program self-consistently.

Publication Date



© 2009 IOP Publishing Ltd. All rights reserved.

This is an author-created, un-copyedited version of an article accepted for publication/published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/0264-9381/26/1/015007

Also archived in arXiv:0804.3824 v1 Apr 24, 2008.

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus