A-BHPT-toolkit: Analytic Black Hole Perturbation Theory Package for Gravitational Scattering Amplitudes

TL;DR

This paper introduces A-BHPT-toolkit, a software package that facilitates analytic and numerical calculations of gravitational scattering amplitudes in black hole perturbation theory using the MST method, aiding research in gravitational physics.

Contribution

It provides the first public toolkit for computing gravitational scattering amplitudes in black hole perturbation theory with both analytic and numerical capabilities.

Findings

Computed scattering phase shifts for massless fields up to third PM order.

Compared analytic results with exact numerical solutions, validating the toolkit.

Enabled new insights into gravitational scattering by rotating black holes.

Abstract

Applications of effective field theory (EFT) and scattering amplitudes to gravitational problems have recently produced many unique results that advanced our understanding of the dynamics of compact binaries. Many of these results were made possible by comparing gravitational scattering amplitudes in EFT with exact expressions from general relativity. However, the latter expressions are not easily available as they require intricate solution techniques for the Teukolsky master equation, such as the Mano-Suzuki-Takasugi (MST) method. In this paper, we develop and present the first public package that enables computations of gravitational scattering amplitudes in black hole perturbation theory within the MST framework. Our package supports both analytic computations to a given post-Minkowskian (PM) order in the low-frequency limit and exact numerical computations for an arbitrary frequency of the perturbing field. As an application, we compute scattering phase shifts and inelasticity parameters for massless spin - 0, 1, and 2 fields resulting from scattering off a rotating Kerr black hole through the third PM order and compare these results with the exact numerical solutions.