Recipes for computing radiation from a Kerr black hole using Generalized SasakiNakamura formalism: I. Homogeneous solutions
Abstract
Central to black hole perturbation theory calculations is the Teukolsky equation that governs the propagation and the generation of radiation emitted by Kerr black holes. However, it is plagued by a longranged potential associated to the perturbation equation and hence a direct numerical integration of the equation is challenging. Sasaki and Nakamura devised a formulation that transforms the equation into a new equation that is free from the issue for the case of outgoing gravitational radiation. The formulation was later generalized by Hughes to work for any type of radiation. In this work, we revamp the Generalized SasakiNakamura (GSN) formalism and explicitly show the transformations that convert solutions between the Teukolsky and the GSN formalism for both ingoing and outgoing radiation of scalar, electromagnetic and gravitational type. We derive all necessary ingredients for the GSN formalism to be used in numerical computations. In particular, we describe a new numerical implementation of the formalism, GeneralizedSasakiNakamura.jl, that computes homogeneous solutions to both perturbation equation in the Teukolsky and the GSN formalism. The code works well at low frequencies and is even better at high frequencies by leveraging the fact that black holes are highly permeable to waves at high frequencies. This work lays the foundation for an efficient scheme to compute gravitational radiation from Kerr black holes and an alternative way to compute quasinormal modes of Kerr black holes.
 Publication:

arXiv eprints
 Pub Date:
 June 2023
 DOI:
 10.48550/arXiv.2306.16469
 arXiv:
 arXiv:2306.16469
 Bibcode:
 2023arXiv230616469L
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 31 pages, 12 figures