Conserved currents associated with conformal symmetry in linearized gravity

@misc{toth2026conserved,
  title = {{Conserved currents associated with conformal symmetry in linearized gravity}},
  author = {Gabor Zsolt Toth},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39476},
  eprint = {2609.39476},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39476},
}

TY  - UNPB
TI  - Conserved currents associated with conformal symmetry in linearized gravity
AU  - Gabor Zsolt Toth
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39476
UR  - https://arxiv.org/abs/2609.39476
AB  - Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor T_lg^ab we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor M_lg^abc and a dilatation current D_lg^a, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor C_lg^ab, accompanying T_lg^ab, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of M^abc, D^a and C^ab tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.
ER  -