Transition from inspiral to plunge into a highly spinning black hole

TL;DR

This paper extends the Ori-Thorne-Kesden method to describe the transition from inspiral to plunge into highly spinning black holes, revealing different governing equations depending on the spin magnitude and analyzing the implications for black hole extremality.

Contribution

It introduces a unified framework for modeling the inspiral-plunge transition across all black hole spins, including near-extremal cases, and links the transition dynamics to special mathematical equations.

Findings

Transition governed by Painlevé transcendent for moderate/high spins

Self-similar Korteweg-de Vries solution for near-extremal spins

Extremal black holes cannot be spun up arbitrarily due to superradiance

Abstract

We extend the Ori-Thorne-Kesden procedure to consistently describe the non-quasi-circular transition around the ISCO from inspiral to plunge into a black hole of arbitrary spin, including near-extremal. We identify that for moderate or high spins the transition is governed by the Painlev\'e transcendent equation of the first kind while for extremely high spins it is governed by a self-similar solution to the Korteweg-de Vries equation. We match the transition solution at leading order in the high spin limit with the analytical quasi-circular inspiral in the near-horizon region. We also show that the central black hole of an extreme mass ratio binary has a near-extremality parameter that scales at least as the mass ratio due to superradiant gravitational wave emission, which excludes extremely high spins.