Optimizing Calculation of the Squared Weyl Tensor on xCOba

[Miguel Yulo]

Hello,

I am new to using xCoba. I am trying to calculate the Squared Weyl Tensor for a specific Kerr-like metric in Boyer-Lindquist coordinates.

I have used and adapted some of the template notebooks of Dr.Anagnostopoulos openly accessible from https://www.physics.ntua.gr/konstant/GR/videos.html.

I did this calculation for the Kerr metric, and got a result within seconds. However, the specific metric I am now using is quite a bit more complicated than the regular Kerr metric, and thus the calculation has been running for hours.

I attempted inserting  Weyl[CD][-\[Mu],-\[Nu],-\[Rho],-\[Lambda]] Weyl[CD][\[Mu],\[Nu],\[Rho],\[Lambda]]  within a Parallelize[] command, but got the message that parallelization was not applicable:

 Parallelize: Weyl[CD][-\[Mu],-\[Nu],-\[Rho],-\[Lambda]] Weyl[CD][\[Mu],\[Nu],\[Rho],\[Lambda]] cannot be parallelized; proceeding with sequential evaluation.

I would like to ask if there is a better way to make the calculation run faster, and perhaps use more of my computer's power.

I have attached my notebook to this post.

Thank you very much in advance!

[Jose]

Hi,

This is a frequent discussion in this forum: Working with complicated metrics is slow. The main problem is usually that SetCMetric and MetricCompute try to simplify the intermediate results at every step of the computation, using the function given by the CVSimplify option, which defaults to the function stored in the $CVSimplify global variable, which by default is Simplify. For moderately non-trivial metrics, the curvature tensors can have very complicated components, so it takes a long time to simplify them with Simplify. Using a lighter simplifier like Together is usually faster, but tends to give much larger results. Using Identity would be even faster, but generally gives enormous results. Usually, however, it is better to get quickly a result and then spend time simplifying individual components of the result. You need to decide what works better for you.

See for example a similar situation in

https://groups.google.com/g/xact/c/6lrcQOVLMRU/m/-grGQoCuAQAJ?hl=en

I attach your notebook with a computation of your Weyl^2 object. But it has no simplification, so it takes 111MB of space. I'm not sure how much this can be simplified...

Cheers,

Jose.

[Miguel Yulo]

Hi,

Thank you for clarifying this. Also appreciate you rewriting the notebook for the computation. I will indeed have to decide what to do with such a large expression.

Best regards,

Miguel