Hi,
Recently Ian Hinder and I have created an arrangement of thorns called EinsteinExact which provide some exact solutions for use in Cactus. The scope of these thorns is similar to that of the Exact thorn but with some notable improvements:
* The extrinsic curvature is computed symbolically rather than using finite differencing so it should be accurate to within roundoff. This means that EinsteinExact is more exact than Exact. * The solutions used in EinsteinExact come from a database of metrics which have been correctness-tested, e.g., by checking symbolically that they are a solution of the Einstein equation. * EinsteinExact is written in Mathematica and uses Kranc, so the raw source is very small (~250 lines) and easy to understand. * Adding a spacetime is as simple as typing the components of the metric into Mathematica.
So far, the spacetimes included are Minkowski, Kerr-Schild, gauge wave and shifted gauge wave, but the list can easily be extended in the future. There is also support for arbitrary rotations, using the same conventions as the Exact thorn uses. We have not yet included the other transformations supported by Exact, but they shouldn't be difficult to add.
We have checked that for these spacetimes the Exact solutions converge to the EinsteinExact solutions at the correct finite differencing order used by Exact.
We would like to propose the EinsteinExact arrangement for inclusion in the EinsteinToolkit. If you would like to try it out, you can get it using:
git clone --recursive git://github.com/barrywardell/EinsteinExact
Any comments or suggestions are welcome.
Regards, Barry