[Users] a question about the WeylScal4 thorn

Ian Hinder ian.hinder at aei.mpg.de
Tue Jun 23 12:35:34 CDT 2015

On 23 Jun 2015, at 16:38, Vassilios Mewes <vassilios.mewes at uv.es> wrote:

> Hello all,
> I have a quick question about the GW extraction using the WeylScal4 thorn in the Einstein Toolkit.
> The thorn uses the description of http://journals.aps.org/prd/pdf/10.1103/PhysRevD.65.044001 to calculate the Weyl scalar, right? (which seems to be the same as described in the numerical relativity book by Baumgarte and Shapiro, if I am not mistaken)..
> Is this way of calculating the Weyl scalar equivalent to the one that uses the electric and magnetic part of the Weyl tensor (like for instance in the Book by Alcubierre or in i.e. http://arxiv.org/pdf/0910.3803v1.pdf)?

Yes, it is equivalent.  

> It seems that the method implemented in the ET has extra factors of R_{ijkl} compared to the one using the electric and magnetic parts of the Weyl tensor.

The EM method is, loosely,

	E - i B = Ricci - (...K...) + curl K

	Psi4 = (E - i B) mBar mBar

and the direct method is

	Psi4 = C n mBar n mBar

The contraction of C with the ns gives you combinations of the Ricci and K.  During our work on http://arxiv.org/abs/1105.0781, we directly compared WeylScal4 against the Psiclops code (https://bitbucket.org/llamacode/ctgamma/src/master/Psiclops/), which implements both methods, and checked that the results were the same, and also converged to the correct answer for a nontrivial exact solution (I think Kerr, but don't remember the details).  We derived the equations used in both methods, and checked that the source code in both thorns reflected the equations we derived.

So the quick answer is "yes, the methods are the same, and I believe strongly that Psi4 in WeylScal4 is correct".

The long answer would start with another question, which is "which term exactly do you think is wrong?".

Ian Hinder

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