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arXiv · 2609.25281

Black Hole Perturbation Toolkit: Low frequency and post-Newtonian expansions

Jakob Neef·Chris Kavanagh·Adrian Ottewill
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Abstract

The Teukolsky and SpinWeightedSpheroidalHarmonics packages of the black hole perturbation toolkit (BHPT) are one of the main public libraries to compute numerical solutions to the Teukolsky equation and related quantities. This work is a companion paper presenting their new and improved weak-field analytic functionality focusing on post-Newtonian expansions. The Teukolsky package now allows users to independently extract multiple useful quantities, such as the so called MST coefficients, renormalized angular momentum, amplitudes of the radial functions or the phase shift as a low frequency/PM expansion. It also provides PN expansions of the homogeneous radial functions or - for circular orbits in Kerr - inhomogeneous amplitudes, as well as energy and angular momentum fluxes at infinity and the horizon. All quantities can be computed to state of the art precision on regular laptops. It also provides a suite of tools for post-Newtonian self force computations and updates the analytic functionality of the SpinWeightedSpheroidalHarmonics package. Computations are possible both for specific and generic spin weight $s$ and harmonic mode numbers $\ell$ and $m$. This package paves the way for intensive high-order post-Newtonian self-force calculations at the forefront of waveform modelling of small mass ratio black hole binaries, as well as giving widely useful low-frequency expansions for black hole perturbation theory. All functions described in this paper are available in BHPT versions Teukolsky v.1.2 and SpinWeightedSpheroidalHarmonics v.1.1.

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Jakob Neef, Chris Kavanagh, Adrian Ottewill. 2026-09-21. Black Hole Perturbation Toolkit: Low frequency and post-Newtonian expansions. https://arxiv.org/abs/2609.25281

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