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Regular second-order perturbations of binary black holes in the extreme mass ratio regime. (English) Zbl 1157.83015

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.

MSC:

83C57 Black holes
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
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