Natural equation

A field equation built on a natural bundle — one that transforms functorially under diffeomorphisms of the underlying spacetime manifold — which is the technical, category-theoretic content behind what physicists informally call "general covariance."

Matters to this vault as the framework Weatherall and Eleanor March's 2026 paper works within throughout: its central project is showing how close natural equations can come to having a well-posed initial-value problem (never exactly, per a companion paper, but "almost" for physically important cases like Einstein's equation), building on Geroch's technical apparatus and addressing, in spirit, the Kretschmann objection that covariance alone is not a substantive constraint.

References

• claim-march-weatherall-minimal-coupling-unique-up-to-isomorphism
• claim-march-weatherall-causal-cones-coincide-with-metric-lightcones
• claim-march-weatherall-natural-maximal-hyperbolizations-satisfy-dominant-energy-condition
• claim-march-weatherall-hyperbolization-tensor-divergence-free-by-naturality