Scri

This is a Julia package for working with gravitational and electromagnetic waveforms at future or past null infinity, including transformations under the BMS group. The package is designed to be fast, accurate, and easy to use, and is intended to be a useful tool for researchers in numerical relativity and gravitational-wave astronomy.

Installation

From the Julia REPL, press ] to enter the package manager, then run:

pkg> add https://github.com/moble/Scri.jl

Or equivalently, from any Julia session:

using Pkg
Pkg.add(url="https://github.com/moble/Scri.jl")

Example Usage

The main functionality of the package is provided by the transform! function, which takes as input a set of waveforms represented as a three-dimensional array of complex numbers, the corresponding times, and a set of parameters specifying the BMS transformation to be applied, and returns the transformed waveform and the corresponding retarded times in the new frame.

using Quaternionic
using Scri

# Construct random test data
ℓₘₐₓ = 8
data_components = ("h", "Psi4")
Nᵗ = 10_000
Nᵐ = (ℓₘₐₓ + 1)^2
Nᵈ = length(data_components)
data = randn(ComplexF64, Nᵐ, Nᵗ, Nᵈ)
t = collect(LinRange(-50, 5000, Nᵗ))

# Construct a random-ish BMS transformation
v⃗ = 1e-3 * normalize(randn(QuatVecF64))
R = randn(RotorF64)
α = 1e-3 * randn(ComplexF64, Nᵐ)

# Perform the transformation
data′, t′ = Scri.transform!(data, t, v⃗, R, α; data_components)

Note a few very important points:

1. The transform! function modifies its input data in place, and also returns the modified version. (The exclamation mark is the Julia convention for indicating that the function modifies its arguments in place.) This is done for performance reasons, to avoid unnecessary allocations. If you want to keep the original data, you can make a copy before calling transform! with the Base.copy function.
2. The input data must be shaped as a three-dimensional array, with the first dimension corresponding to the mode weights, the second dimension corresponding to time, and the third dimension corresponding to the different field components.
3. The first index of the data array represents mode weights starting with $ℓ=0$, even for fields with nonzero spin weight. The mode weights are ordered in the standard way, with the $m=-ℓ$ mode first and the $m=+ℓ$ mode last, then incrementing $ℓ$.
4. The third index of the data array must correspond to the data_components argument. That is, it must have the same length, and describe the components in the same order.
5. In this example, the supertranslation α was constructed randomly, and doesn't represent a real-valued function. Internally, transform! automatically imposes the reality condition on α by averaging each mode with its complex-conjugate partner.

Name and Pronunciation

"Scri" (rhymes with "sky") is the pronunciation of the character $ℐ$ (script I; given by the latex \mathscr{I}), which is the notation for null infinity in the theory of asymptotically flat spacetimes, introduced by Penrose in 1963 and now standard throughout the literature. We usually distinguish between future null infinity, denoted $ℐ⁺$, and past null infinity, denoted $ℐ⁻$. This package defaults to working with future null infinity, since the author's primary interest is in the emission of gravitational waves from isolated systems, but there are options to model past null infinity, to investigate the detection of incoming radiation.