Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime

TL;DR

This paper introduces a hyperboloidal compactification method for Teukolsky equations in Kerr spacetime, enabling accurate extraction of gravitational waveforms at null infinity from extreme-mass-ratio inspirals.

Contribution

The paper presents a novel hyperboloidal layer technique that includes null infinity in numerical simulations of Kerr spacetime, improving waveform extraction accuracy.

Findings

Successful extraction of gravitational waveforms at null infinity.

Validation of the hyperboloidal layer method against previous results.

Enhanced accuracy and efficiency demonstrated through tests.

Abstract

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.