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I am currently re-reading through Carroll's text on SR and there is a curious comment on p24 that intrigues me. Carroll says that the *only* tensors in SR which are invariant are the Kronecker delta, the Levi-Civita tensor, and the metric tensor. In GR, the latter is no longer invariant so there are only two invariant tensors.

Carroll says "we won't prove it" but I'm dying to see the proof, which I've spent a few hours trying to derive. The internet has also been little help, aside from this topic which doesn't really give an answer:

https://www.physicsforums.com/showthread.php?t=344626

So how do we show that there are no other invariant tensors?

Thanks!