Binary black hole merger in the extreme mass ratio limit: a multipolar analysis of the inclined orbit case

Abstract

We compute the gravitational waveform emitted during the transition from quasi-spherical inspiral to plunge, merger and ringdown for a system of two black holes in the extreme mass ratio limit, where the primary is spinning and the secondary is represented by a nonspinning point-particle inspiralling along inclined orbits. The point-particle dynamics is described via a Hamiltonian formalism and the transition is driven by an effective-one-body like radiation reaction force. The gravitational waveform is obtained solving numerically, in the time-domain, the Teukolsky equation with a $\hat{I}´$-like source. The waveform is systematically characterized varying the black hole spin magnitude between $(0,0.9)$ and the inclination angle of the orbit between $(0,\ddot{I}€)$. We consider all multipoles up to $\ell =4$ and compute the energy and angular momentum losses during the plunge. The impact of the $m\ne \ell$ modes grows as the inclination angle is increased. We also use our framework to quantify the accuracy of the approximate inspiral-merger-ringdown waveform for an inclined orbit that can be obtained by applying a suitable time-dependent rotation to a given spin-aligned waveform with approximately consistent (but constant) spin-orbit coupling.

32 pages, 27 figures. Submitted to Phys. Rev. D