Transition from Inspiral to Plunge: A Complete Near-Extremal Trajectory and Associated Waveform

TL;DR

This paper extends the Ori and Thorne method to accurately model the transition from inspiral to plunge for near-extremal spinning black holes, providing a complete trajectory and waveform prediction for extreme mass ratio inspirals.

Contribution

It introduces a generalized transition framework for near-extremal black holes, accounting for different scaling regimes and refining the assumptions about energy and angular momentum evolution.

Findings

Identifies three scaling regimes based on mass ratio and spin

Confirms quasi-circular approximation remains valid during transition

Provides an algorithm for full waveform computation in high-spin EMRIs

Abstract

We extend the Ori and Thorne (OT) procedure to compute the transition from an adiabatic inspiral into a geodesic plunge for any spin, with emphasis on near-extremal ones. 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 resultant gravitational waveform in the high spin limit.