GRworkbench software for numerical differential geometry & visualization

GRworkbench

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Source

The GRworkbench source is on GitHub: https://github.com/andrewmoylan/grworkbench

Summary

GRworkbench is software for numerical operations in, and visualisation of, space-times in general relativity, and differential manifolds in general. For my Honours thesis, I (with Antony Searle) developed a new version of GRworkbench in C++. The new version included improvements directed towards enabling numerical experiments within GRworkbench.

Here is GRworkbench visualising the world-lines of the end-mirrors (light blue) and photons (yellow; numerically determined null geodesics) of an idealised interferometer in the vicinity of the event horizon of a Schwarzschild black hole (blue sphere):

Usage

Here's how you might use GRworkbench to visualise two different time-like geodesics passing through the same point in the Schwarzschild space-time:

In the above example, "C" is a chart corresponding to the usual Schwarzschild coordinates. GRworkbench automatically handles multiple overlapping charts and the transformations between them. It knows about a variety of standard space-times, with the possibility of adding support for more. It can visualise any parameterised 1- or 2-dimensional surfaces.

More information

See my scientific articles about GRworkbench.

The development of GRworkbench is an ongoing project at The ANU. See the ANU GRworkbench project page for the latest news, and to download any available versions.

The lax language

The language used above in the textual interface to GRworkbench is "lax". It is an experimental interpreted functional scripting language designed and written by myself and Antony Searle. We learned a lot writing it, most importantly: don't decide to write your own language lightly. That said, lax has some neat features; read on to learn about how it works.

In lax,

• functions are called by separating the function and its argument with a space;
• functions are defined inside { } curly brackets;
• the argument to the first enclosing pair of { } curly brackets is a ? question mark;
  • the argument to the next enclosing pair of { } curly brackets is a :? colon preceding a question mark; and
• order of evaluation is specified using ( ) parentheses as in most languages:

Underneath, lax is largely based on the SKI combinator calculus, in which the three basic "combinators" S, K, and I, are defined by

• S a b c = (a c) (b c) = a c (b c),
• K a b = a, and
• I a = a.

Internally to lax, functions are expressed in terms of these combinators:

By Andrew Moylan (email).