Lousto, Carlos O.; Nakano, Hiroyuki Regular second-order perturbations of binary black holes in the extreme mass ratio regime. (English) Zbl 1157.83015 Classical Quantum Gravity 26, No. 1, Article ID 015007, 24 p. (2009). Summary: In order to derive the precise gravitational waveforms from 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 the \(T_{\mu \nu }\) and 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 Dirac’s delta and that perturbations are regular at the particle location. We introduce an asymptotically flat gauge for the \(\ell = 0\) and \(\ell = 1\) modes to compute the (leading radiative) second-order \(\ell = 2\) waveforms in the head-on collision case. Cited in 1 Document MSC: 83C57 Black holes 83C25 Approximation procedures, weak fields in general relativity and gravitational theory PDFBibTeX XMLCite \textit{C. O. Lousto} and \textit{H. Nakano}, Classical Quantum Gravity 26, No. 1, Article ID 015007, 24 p. (2009; Zbl 1157.83015) Full Text: DOI arXiv