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Timeline for Torsion tensor symmetrisation

Current License: CC BY-SA 4.0

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Mar 11, 2021 at 16:51 vote accept Jorge Casajus
Mar 11, 2021 at 7:37 vote accept Jorge Casajus
Mar 11, 2021 at 16:51
Mar 10, 2021 at 15:00 history tweeted twitter.com/StackPhysics/status/1369664365054599181
Mar 10, 2021 at 11:46 comment added Qmechanic Related: physics.stackexchange.com/q/306927/2451
Mar 10, 2021 at 11:44 history edited Qmechanic
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Mar 10, 2021 at 11:20 comment added Eletie I'll write a full answer as it's just some pretty messy indices manipulations.
Mar 10, 2021 at 11:19 answer added Eletie timeline score: 1
Mar 10, 2021 at 10:45 comment added Jorge Casajus I got it from Hobson's General Realativity: An introduction for physicists. It's equation 3.11, and this is exercise 3.8, which also requires to prove that equation yourself (something I thought I had done right)
Mar 10, 2021 at 10:40 comment added Eletie Just to check, do you have a source for your first equation? Usually one writes $\Gamma = \{ \} + K$, with K being the contorsion tensor defined here en.wikipedia.org/wiki/Contorsion_tensor this slightly differs from your definitions.
Mar 10, 2021 at 10:29 comment added Jorge Casajus And... Should I do that multiplying by the covariant or contravariant components of the metric tensor? If so, would't they still cancel out since the symmetries in the metric tensor won't induce any extra sign changes?
Mar 10, 2021 at 10:24 comment added Eletie Yes your hunch is right: the symmetry properties only apply for the specific index combination, so its just a case of manipulating the indices to match the desired form.
Mar 10, 2021 at 9:37 history asked Jorge Casajus CC BY-SA 4.0