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    Noether's second theorem yields differential identities (... — Carmelics
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    Challenges→Energy-momentum conservation laws for general coordinate transformations and internal Lorentz transformations of tetrads can be derived as a special case of Noether's second theorem.

    Noether's second theorem yields differential identities (Bianchi-type), not genuine conservation laws with locally conserved currents in curved spacetime.

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    Reasons For

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    Reason for
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    • 1.Noether's second theorem applies to gauge theories with off-shell symmetries, yielding identities among equations of motion, not independent conservation laws.
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    • 2.In curved spacetime, the covariant divergence of the stress-energy tensor vanishes identically (Bianchi identity), making it a constraint rather than a conservation law.
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    • 3.Genuine local conservation requires a globally defined current density; curved spacetime lacks global symmetries needed for Noether's first theorem to apply.
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    Reasons Against

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    • 1.Differential identities ARE conservation laws: they express continuity equations relating energy-momentum flow to curvature, physically meaningful locally.
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    • 2.Quasilocal currents (e.g., Komar integral) rigorously define conserved quantities in curved spacetime without requiring global symmetries, contradicting the claim.
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    • 3.Noether's second theorem generates the Bianchi identities precisely because they govern actual physical conservation of energy-momentum in general relativity.
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    Related

    Differential identities ARE conservation laws: they express continuity equations...Energy-momentum conservation laws for general coordinate transformations and int...Genuine local conservation requires a globally defined current density; curved s...In curved spacetime, the covariant divergence of the stress-energy tensor vanish...
    +3 moreShow less
    Noether's second theorem applies to gauge theories with off-shell symmetries, yi...Noether's second theorem generates the Bianchi identities precisely because they...Quasilocal currents (e.g., Komar integral) rigorously define conserved quantitie...

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