# Spin and Quadrupole Couplings for High Spin Equatorial Intermediate Mass-ratio Coalescences

## TL;DR

This paper provides analytic results on spin and quadrupole couplings for high spin black hole orbits, aiding the modeling of gravitational wave signals from intermediate mass-ratio coalescences.

## Contribution

It introduces leading-order analytic calculations of spin and quadrupole effects in equatorial orbits near highly spinning black holes, neglecting self-force.

## Key findings

- Analytic expressions for spin couplings near extremal black holes.
- Identification of critical behavior near minimal angular momentum.
- Discussion of finite size effects in gravitational wave modeling.

## Abstract

Intermediate mass-ratio coalescences are potential signals of ground-based and space-based gravitational observatories. Accurate modeling of their waveforms within general relativity can be achieved within black hole perturbation theory including self-force and finite size effects. In this paper, we present analytic results to the Teukolsky perturbation of equatorial orbits in the near-horizon region of an extremely high spin black hole including spin coupling and finite size effects at leading order in the high spin limit while neglecting the self-force. We detail the critical behavior occuring close to the smallest specific angular momentum, and we discuss features of spin and quadrupole couplings.