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Abstract

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by
"stitching" together a long inspiral waveform from a sequence of waveform
snapshots, each of which corresponds to a particular geodesic orbit. We show
that the complicated total waveform can be regarded as a sum of "voices." Each
voice evolves in a simple way on long timescales, a property which can be
exploited to efficiently produce waveform models that faithfully encode the
properties of EMRI systems. We look at examples for a range of different
orbital geometries: spherical orbits, equatorial eccentric orbits, and one
example of generic (inclined and eccentric) orbits. To our knowledge, this is
the first calculation of a generic EMRI waveform that uses strong-field
radiation reaction. We examine waveforms in both the time and frequency
domains. Although EMRIs evolve slowly enough that the stationary phase
approximation (SPA) to the Fourier transform is valid, the SPA calculation must
be done to higher order for some voices, since their instantaneous frequency
can change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f <
0$). The approach we develop can eventually be extended to more complete EMRI
waveform models, for example to include effects neglected by the adiabatic
approximation such as the conservative self force and spin-curvature coupling.