Characterize genuine symmetries among field transformations in linearised gravitational energy constructions

Determine which field transformations introduced in the Bessel–Hagen-motivated classification of linearised gravitational energy-momentum tensors are genuine symmetries of the action.

Background

The paper compares its localizability result with the classification of Taylor and Baker, who obtain families of linearised gravitational energy-momentum tensors by allowing boundary-equivalent Lagrangians and translation-proportional field transformations. Although some members of that family are simultaneously symmetric and traceless, none is gauge invariant. The cited classification does not resolve which of the allowed field transformations correspond to genuine symmetries of the action, leaving this as an unresolved structural question relevant to the interpretation of the resulting currents.

References

Their classification leaves open which field transformations are genuine symmetries of the action.

— Bessel-Hagen currents, reducibility charges, and local gravitational energy  (2610.13700 - Hobson et al., 9 Oct 2026) in Section 6, Discussion

Gauge theories of gravity with both internal and spacetime symmetries, such as Weyl gauge theory and its extended form raise a further question. An effectively internal sector, for example the dilation field-strength sector, might admit a strong local current of the Maxwell type, whereas the diffeomorphism and local Lorentz sectors might have local obstructions together with independent reducibility charges.

— Bessel-Hagen currents, reducibility charges, and local gravitational energy  (2610.13700 - Hobson et al., 9 Oct 2026) in Section 6, Discussion