XCoba do not compute Riemann tensor

[Tommaso De Lorenzo]

Dear all,

I'm new in xAct as well as in this group.

I would like to ask you a very basic question: I'm trying to compute different geometric object for a specific "Kerr-like" metric; in particular I would like to find the Kretschmann scalar.

However, when I ask xCoba to compute Riemann tensor, it runs without giving a result, but giving me "Time spent on a transformation exceeded 300.` seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification."

The weird part of the story is that it is able to compute Christoffel symbols in a reasonable time, and Riemann tensor in nothing but derivatives and products of Christoffel symbols.

So I would like to know if someone can explain me where the computation can break down and if there is the possibility to solve it to arrive computing the curvature scalar. Maybe relaxing symplification rules, or imposing something else that I do not know.

I'm attaching my simple notebook, which is just the one I found in the xCoba web page modified for my purpose. Maybe the problem is in the fact that I have too many free parameters?

Thank you very much for your help,

Tommaso

[mcnees]

Hi Tommaso,

You should consider making a change of variables like u = \cos\theta. These calculations take significantly longer with trig functions in the metric. 

Best,

Bob

[Tommaso De Lorenzo]

Dear Bob,

thank you very much for your suggestion. However, I implemeted the change of variables, but unfortunately it did not significantly help the computation.

Do you have any other idea?

Best,

Tommaso

[Jose]

Hi,

MetricCompute tries to simplify intermediate expressions during the computation. This is controlled with the option CVSimplify of MetricCompute, which defaults to $CVSimplify, which initially is Simplify. For hard computations like the one you have, it is usually better to avoid Simplify, which can be very slow sometimes, and has the 300 seconds TimeConstraint (this is an option of Simplify itself). In my experience, Together does a better job balancing the size-reduction of expressions and giving a result in reasonable time, mainly when the input expressions are given in terms of complicated rational functions.

Another possibility is to use directly CVSimplify -> Identity, which will do no simplification whatsoever. You will get a huge answer that you have to simplify by hand later, but you'll get it quickly (provided your computer has enough memory to store that answer). Sometimes I ended up with this approach and then analyzing the result numerically.

Let me also mention that simplification of different components of a tensor is done independently, so if you have a machine with multiple cores then you can parallelize the simplification operation. Use the option Parallelize -> True in MetricCompute.

I recommend to have a look at the "hard examples" 4.4, 4.5 and 4.6 of the notebook xAct/Documentation/English/xCobaDoc2.nb .

Hope that helps,
Jose.

[Tommaso De Lorenzo]

Hi Jose,

this is exactly what I was looking for. I need to treat the result numerically, so I do not care about the nicest analytical expression.

Now it computer All in less the 6 seconds.

Thank you very much,

Tommaso