Online Christoffel Symbols Calculator

[Dhananjhay]

TL;DR Summary

I've launched the very first mathematical web application with a Graphical User Interface (GUI) capable of calculating Christoffel Symbols (both first and second kinds) and associated Tensors (Riemann, Ricci, and Einstein) in a matter of just a few seconds!

Link: https://christoffel-symbols-calculator.com/

I would love to hear from you if you have any suggestions, feedback, or criticism. The goal is to build better and more sophisticated software that would push the boundaries of research in astrophysics!

 

[berkeman]

Thread is in Moderation for review by the Mentors.

UPDATE: After a Mentor discussion, this thread is reopened. Thanks for your patience.

 

[fresh_42]

Link: https://christoffel-symbols-calculator.com/

I would love to hear from you if you have any suggestions, feedback, or criticism.

Me, too. Please check validity and reliability and let us know your results!

 

[strangerep]

TL;DR Summary: I've launched the very first mathematical web application with a Graphical User Interface (GUI) capable of calculating Christoffel Symbols (both first and second kinds) and associated Tensors (Riemann, Ricci, and Einstein) in a matter of just a few seconds!

Link: https://christoffel-symbols-calculator.com/

How do I change to spherical coordinates, i.e., $r, \theta, \phi$ ?
(Your calculator seems to insist on using Cartesian coordinates.)

 

[Dhananjhay]

Thank you for your comment! (x,y,z) don't necessarily represent Cartesian coordinates. They are just symbols (more specifically, components of a contravariant vector) and can be used contingent on your needs. `x` means the the first coordinate, `y` means the second coordinate, and `z` means the third coordinate. In your case, I would just replace `r` by `x`, `θ` by `y`, and `Φ` by `z`. I hope this clears your doubt.

 

[strangerep]

Thank you for your comment! (x,y,z) don't necessarily represent Cartesian coordinates. [...]

Yes, that's what I figured. But,... it's a bit sad.

Most other Einstein calculation packages allow one to use one's own variables of choice. Many can also generate latex output for, e.g., easy inclusion in publishable papers.

 

[Dhananjhay]

Let me see what I can do! But thank you very much for your comment, this is exactly what I needed! I've noted down your concerns and hopefully, in the next release you should have access to the variables of your own choice and a latex output.

 

[Dhananjhay]

Yes, that's what I figured. But,... it's a bit sad.

Most other Einstein calculation packages allow one to use one's own variables of choice. Many can also generate latex output for, e.g., easy inclusion in publishable papers.

Hello! Thanks to your earlier comment, I've now added a new feature to the software that will allow users to choose the coordinate system of their choice. You can also export the results to LaTeX. Both excellent suggestions/feedback!

A reliability test was conducted on the software and the results have been attached to this comment in a form of a txt file. The space-time models were taken from the paper Catalogue of Spacetimes (Thomas Müller & Frank Grave, Nov 2010).

Please let me know if you have any more suggestions, feedback or criticism!