Metric-Affine Gauge Theory of Gravity

A framework for gravity, founded on Hehl, McCrea, Mielke & Ne'eman's 1995 Physics Reports review "Metric-Affine Gauge Theory of Gravity" (arXiv:gr-qc/9402012), that builds gravitational field equations by gauging the Poincaré or full affine symmetry group rather than by positing geometric equivalences directly. Varying its action with respect to the affine connection, separately from the co-frame, produces a second set of field equations coupling matter's spin, dilation, and shear currents ("hypermomentum") to torsion and non-metricity — a sector Kartik Tiwari (2026) argues is missing from standard Geometric Trinity equivalence arguments. Matters to this vault as the technical machinery behind an active challenge to a well-known equivalence result in classical gravitational theory.

References

• claim-gauge-gravitys-hypermomentum-challenge-conditionally-breaks-geometric-trinity-equivalence

• claim-hypermomentum-challenge-latent-in-mag-since-1995-explicit-2024

• claim-hehl-1995-already-defines-hypermomentum-current-coupled-to-connection

• Related hubs: entity-geometric-trinity · entity-hypermomentum · entity-friedrich-hehl

• Founding primary partially read: Hehl, McCrea, Mielke & Ne'eman, Physics Reports 258(1-2):1-171 (1995), arXiv:gr-qc/9402012 — see question-verify-hypermomentum-challenge-1995-2024-priority-claim.

• 2026-10-10: The founding review's own abstract and Introduction were fetched directly and confirmed the hypermomentum current was defined specifically to couple to the connection, generating the independently-varied field-equation sector the modern "hypermomentum challenge" turns on — the mechanism was named in 1995, not invented in 2024 (claim-hehl-1995-already-defines-hypermomentum-current-coupled-to-connection). arXiv's copy of the review is only a 6-page stub, so this is confirmed from the Introduction's own description of Chapter 5, not from Chapter 5 itself.