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3 months ago in Thermodynamics By Usha K

What does noether’s theorem give you in general relativity?

Noether's theorem says every symmetry gives a conserved quantity. GR is diffeomorphism invariant—that's a huge symmetry. So where's the conserved energy?

GeneralRelativity

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By Omar Answered 2 months ago

This troubled Einstein too. The issue: diffeomorphism invariance is a gauge symmetry. The conserved currents it generates vanish "on-shell" when the field equations hold. That means gravitational energy isn't localizable; you can't say "here's exactly 5 joules of gravity in this cubic meter." But you can define global conserved quantities for spacetimes that are asymptotically flat. That's the ADM mass and momentum—the total energy of the entire spacetime, measured at infinity. So conservation exists, but it's global, not local.

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