Edit on GitHub

TeukolskyQNMFunctions

Documentation for TeukolskyQNMFunctions.

TeukolskyQNMFunctions computes the quasinormal modes and eigenfunctions for the spin s Teukolsky equation using a horizon penetrating, hyperboloidally compactified coordinate system. The main advantage of using these coordinates is that the quasinormal wavefunctions are finite valued from the black hole to future null infinity.

Currently, this code uses a Chebyshev pseudospectral method to compute the radial part of the eigenfunctions, and a spectral method to compute the angular part of the eigenfunctions The angular spectral method was originally introduced by Cook and Zalutskiy).

TeukolskyQNMFunctions.TeukolskyQNMFunctions — Module

TeukolskyQNMFunctions.jl computes the quasinormal modes and eigenfunctions for the spin s Teukolsky equation using a horizon penetrating, hyperboloidally compactified coordinate system. The main advantage of using these coordinates is that the quasinormal wavefunctions are finite valued from the black hole to future null infinity.

source
TeukolskyQNMFunctions.F — Method
function F(
    nr::Integer,
    nl::Integer,
    s::Integer,
    l::Integer,
    m::Integer,
    a::T,
    om::Complex{T},
) where {T<:Real}

Compute the absolute difference of Lambda seperation constant for radial and angular ODEs.

source
TeukolskyQNMFunctions.compute_om — Method
compute_om(
    nr::Integer,
    nl::Integer,
    s::Integer,
    l::Integer,
    m::Integer,
    a::Real,
    om::Complex;
    tolerance::Real = 1e6,
    epsilon::Real = 1e-6,
    gamma::Real = 1.0,
    verbose::Bool = false
) where T<:Real

Search for quasinormal mode frequency in the complex plane using Newton's method.

Arguments

  • nr : number of radial Chebyshev collocation points
  • nl : number of spherical harmonic terms
  • s : spin of the field in the Teukolsky equation
  • l : l angular number
  • m : m angular number
  • a : black hole spin
  • om : guess for the initial quasinormal mode
  • tolerance: tolerance for root finder
  • epsilon : derivative finite difference length
  • gamma : search gamma
  • verbose : true: print out intermediate results as searches for root
source
Modules = [TeukolskyQNMFunctions.CustomTypes]
TeukolskyQNMFunctions.Spheroidal.eig_vals_vecs — Method
eig_vals_vecs(nl::Integer, neig::Integer, s::Integer, m::Integer, c::Complex)

Compute the eigenvectors and eigenvalues for the spheroidal equation. Returns eigenvalues λs (smallest to largest), and eigenvectors as an array (access nth eigenvector through v[:,n]); i.e. returns (λs, vs)

source
TeukolskyQNMFunctions.RadialODE.eig_vals_vecs — Method
eig_vals_vecs(
        nr::Integer,
        s::Integer,
        m::Integer,
        a::T,
        om::Complex{T}
    ) where T<:Real

Compute eigenvectors and eigenvalues for the radial equation using a pseudospectral Chebyshev polynomial method. The black hole mass is always one.

source
TeukolskyQNMFunctions.RadialODE.radial_discretized_eqn_a — Method
function radial_discretized_eqn_a(
    nr::Integer,
    s::Integer,
    m::Integer,
    a::T,
    bhm::T,
    om::Complex{T},
    rmin::T,
    rmax::T
) where T<:Real

Discretization that uses fast, well conditioned method of

    S. Olver and A. Townsend, 
    SIAM review, 2013,
    arXiv:1202.1347
source