Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral

TL;DR

This paper derives a closed-form expression for the plunge trajectory from the ISCO in extreme mass ratio inspirals, providing a new way to calculate the associated black-hole ringdown amplitudes and their waveforms.

Contribution

It introduces a novel analytical expression for the ISCO plunge trajectory and its ringdown amplitudes, advancing understanding of waveform modeling in extreme mass ratio inspirals.

Findings

Derived a closed-form solution for the ISCO plunge trajectory.

Provided an analytical expression for the ringdown amplitudes.

Numerically evaluated the ringdown amplitudes for specific cases.

Abstract

An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, and evaluate them numerically.