A New High-Performing Method for Solving the Homogeneous Teukolsky Equation

TL;DR

This paper introduces a novel numerical method based on analytical series expansion that significantly improves the accuracy and efficiency of computing homogeneous solutions of the Teukolsky equation, crucial for modeling gravitational waveforms from EMRIs.

Contribution

The paper presents a new analytical series expansion method that outperforms existing techniques in accuracy and frequency range for solving the Teukolsky equation homogeneous solutions.

Findings

Achieves higher accuracy in homogeneous solutions.

Extends the frequency range for solutions.

Reduces computational time compared to previous methods.

Abstract

The numerical waveforms for the extreme mass-ratio inspirals (EMRIs) require a huge amount of homogeneous solutions of the Teukolsky equation in the frequency domain. The calculation accuracy and efficiency of the homogeneous solutions are the key performance bottleneck in waveform generation. In this paper, we propose a new numerical method based on the analytical series expansion which is most efficient for computing the homogeneous solutions with very high accuracy and a wider frequency range compared with the existing methods. Our new method is definitely useful for constructing the waveform templates of EMRIs.