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Abstract

We extend the Ori and Thorne (OT) procedure to compute the transition from an
adiabatic inspiral into a geodesic plunge for any spin. Our analysis revisits
the validity of the approximations made in OT. In particular, we discuss
possible effects coming from eccentricity and non-geodesic past-history of the
orbital evolution. We find three different scaling regimes according to whether
the mass ratio is much smaller, of the same order or much larger than the near
extremal parameter describing how fast the primary black hole rotates.
Eccentricity and non-geodesic past-history corrections are always sub-leading,
indicating that the quasi-circular approximation applies throughout the
transition regime. However, we show that the OT assumption that the energy and
angular momentum evolve linearly with proper time must be modified in the
near-extremal regime. Using our transition equations, we describe an algorithm
to compute the full worldline in proper time for an extreme mass ratio inspiral
(EMRI) and the full gravitational waveform in the high spin limit.