  We introduce a new kludge scheme to model the dynamics of generic extreme
mass-ratio inspirals (stellar compact objects spiraling into a spinning
supermassive black hole) and to produce the gravitational waveforms that
describe the gravitational-wave emission of these systems. This scheme combines
tools from different techniques in General Relativity: It uses a multipolar,
post-Minkowskian (MPM) expansion for the far-zone metric perturbation (which
provides the gravitational waveforms, here taken up to mass hexadecapole and
current octopole order) and for the local prescription of the self-force (since
we are lacking a general prescription for it); a post-Newtonian expansion for
the computation of the multipole moments in terms of the trajectories; and a BH
perturbation theory expansion when treating the trajectories as a sequence of
self-adjusting Kerr geodesics. The orbital evolution is thus equivalent to
solving the geodesic equations with time-dependent orbital elements, as
dictated by the MPM radiation-reaction prescription. To complete the scheme,
both the orbital evolution and wave generation require to map the
Boyer-Lindquist coordinates of the orbits to the harmonic coordinates in which
the different MPM quantities have been derived, a mapping that we provide
explicitly in this paper. This new kludge scheme is thus a combination of
approximations that can be used to model generic inspirals of systems with
extreme mass ratios to systems with more moderate mass ratios, and hence can
provide valuable information for future space-based gravitational-wave
observatories like LISA and even for advanced ground detectors. Finally, due to
the local character in time of our MPM self-force, this scheme can be used to
perform studies of the possible appearance of transient resonances in generic
inspirals.
