Noether's theorem yields a conservation law for every symmetry. Is that independent of the Lagrangian i.e. when $\mathcal{L}\neq T-V$? In general relativity the integral that is minimised will be the geodesic: $$S=\int ds$$ What form would Noether's theorem take? I am also looking for a proof of this. All the proofs I've seen assume $\mathcal{L}=T-V$.
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