We compute the gravitational waveform emitted during the transition from quasispherical 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 $\delta$-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 $(0,\pi )$. 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.

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• General relativity
• Gravitational waves