In this video, I derive the formulas for the Christoffel symbols corresponding to a diagonal metric tensor/orthogonal curvilinear coordinates, which is a very common metric tensor subtype found in various applications (GR, DiffGeo).
I also apply these formulas to the example of the Schwarzschild metric (at least the ansatz version I derived in my previous GR video). That's why this video will be on both the GR and the Tensor Calculus playlists!
Questions/requests? Let me know in the comments!
Pre-reqs: Previous videos in my Tensor Calculus playlist (if you're mainly here for Tensors): https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
To make sense of my example/the Schwarzschild metric, videos before this one in my GR playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9Dc-vr2nw-UF6PJknfAuJzU
Lecture Notes: https://drive.google.com/file/d/1dX5TjQe5zwkj2bYvfV047xFWxOyYZ2X6/view?usp=drive_link
Special thanks to my Patrons:
Matthew
Patapom
Eugene Bulkin
Andy Johnston
Lina Stritt
Patrick Gibson
Joseph Dubeau
David Johnston