Computing Riemann tensor components for hypothetical spacetimes

[ergospherical]

I'm working on a problem involving some hypothetical spacetimes (i.e. no tables/data-sheets available) and need to calculate a bunch of $R_{\mu \nu \rho \sigma}$ and $R_{\mu \nu}$ values, as well as $R$. The metrics contain some arbitrary functions $f(x^i)$ of the spatial co-ordinates only. There's a little bit of urgency so I can't afford really to spend a great deal of time exploring which packages are best for this task; I hoped that somebody who feels confident with this could advise? Thanks!

 

[Dale]

I use Mathematica for all things math-related. The best Mathematica package I have found is OGRE

https://arxiv.org/abs/2109.04193

 

[vanhees71]

I just finally started to learn Python, and for computer algebra in GR (I guess it can easily be used for other general tensor-analysis work too) I like einsteinpy. Together with jupyter as the frontend it's very nice to work with:

https://einsteinpy.org/

 

[ergospherical]

I use Mathematica for all things math-related. The best Mathematica package I have found is OGRE

https://arxiv.org/abs/2109.04193

Thank you, this looks promising. I noticed in the documentation that it seems to allow you to specify the co-ordinate dependencies of scalar fields, which is one thing I need.

Please allow me some time to install Mathematica and try to run the package!

 

[Orodruin]

I just wrote my own mathematica file to do it for me. Mainly to double check exam answers before putting the exam to the students. It is not that extensive computations after all.

 

[ergospherical]

I use Mathematica for all things math-related. The best Mathematica package I have found is OGRE

https://arxiv.org/abs/2109.04193

It's now working, I can find all of the components.
When I have more time I might experiment with a Python package.

Will shout if problems arise!