Accurate time-domain gravitational waveforms for extreme-mass-ratio binaries

TL;DR

This paper improves time-domain solutions of the Teukolsky equation for extreme-mass-ratio binaries, achieving high accuracy in gravitational waveform calculations, especially for complex high-eccentricity orbits.

Contribution

It introduces a significantly more accurate time-domain method for solving the Teukolsky equation, extending reliable waveform modeling to high-eccentricity orbits where frequency-domain methods struggle.

Findings

Energy fluxes agree within 1% with frequency-domain results for circular orbits.

Method accurately models high-eccentricity 'zoom-whirl' orbits.

Provides gravitational waveforms and strain estimates for complex orbital configurations.

Abstract

The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in Schwarzschild and Kerr, we find agreement to within 1% or better, which we believe can be even further improved. We apply our method to orbits for which frequency-domain calculations have a relative disadvantage, specifically high-eccentricity (elliptical and parabolic) "zoom-whirl" orbits, and find the energy fluxes, waveforms, and characteristic strain in gravitational waves.