Gravitational radiation from Kerr black holes using the Sasaki-Nakamura formalism: waveforms and fluxes at infinity

TL;DR

This paper introduces an efficient new method for solving the Sasaki-Nakamura equation in Kerr black hole perturbation theory, enabling accurate gravitational waveform calculations for both compact and extended sources.

Contribution

A novel integration by parts scheme for the Sasaki-Nakamura formalism that simplifies and accelerates waveform computations across source types.

Findings

Validated against existing literature with excellent agreement

Achieved comparable performance without special optimizations

Applicable to a wide range of source types from compact to extended

Abstract

In linear perturbation theory for Kerr black holes, there are two equivalent formalisms, namely the Teukolsky and the Sasaki-Nakamura (SN) formalism. Typically, one defaults to the Teukolsky formalism, especially when calculating extreme mass ratio inspiral waveforms, and uses the SN formalism when dealing with extended sources, as it offers superior convergence when employing the Green's function method for calculating the inhomogeneous solution. In this work, we present a new scheme for solving the inhomogeneous SN equation, based on integration by parts, that eliminates the extra radial integration step required in the standard formulation to construct the source term for convolution with the SN variable. Our approach enables efficient computations of gravitational waveforms within the SN formalism in all cases, from compact to extended sources. We validate our scheme and code implementation against the literature and find excellent agreement, achieving comparable performance without employing any special optimization techniques.