Teukolsky

Overview

The Teukolsky package computes solutions to the Teukolsky equation, which governs perturbations of the Kerr spacetime for fields of spin-weight s (scalar, electromagnetic and gravitational). It provides the homogeneous radial solutions — the “In” and “Up” functions defined by their boundary conditions at the horizon and at infinity — and point-particle mode data such as amplitudes and energy fluxes for a source on a bound geodesic.

It builds on two other Toolkit packages: SpinWeightedSpheroidalHarmonics for the angular dependence, and KerrGeodesics for the orbital motion of the source.

Further details are available in the source repository and the package page.

Installation

Teukolsky is distributed as a paclet. Once the BHPToolkit paclet server is set up (see Get started), install it by name and load it:

PacletInstall["Teukolsky"]
Needs["Teukolsky`"]

Usage

Compute a homogeneous radial solution and evaluate it at a Boyer-Lindquist radius:

Needs["Teukolsky`"]

s = -2; l = 2; m = 2; a = 0.5; ω = 0.3;
R = TeukolskyRadial[s, l, m, a, ω];

R["In"][10.0]
R["Up"]["RadialDerivative"][10.0]

For a point particle on a bound orbit, build the orbit with KerrGeodesics and pass it to TeukolskyPointParticleMode to obtain the mode amplitudes and fluxes:

Needs["KerrGeodesics`"]

orbit = KerrGeoOrbit[a, 10.0, 0, 1];           (* circular, equatorial *)
mode  = TeukolskyPointParticleMode[s, l, m, 0, 0, orbit];

mode["Fluxes"]
mode["Amplitudes"]

Examples

Worked notebooks covering radial solutions, fluxes and metric reconstruction are in the MathematicaToolkitExamples repository.

Citing Teukolsky

If you use Teukolsky in your research, please acknowledge the Toolkit:

See how to cite for the BibTeX entry and guidance.