Symmetric hyperbolic system

The standard framework, originated by Kurt Otto Friedrichs in 1954, for a system of first-order partial differential equations that guarantees a well-posed initial-value problem — existence, uniqueness, and continuous dependence on initial data — including a finite propagation speed bounded by the system's own characteristic cones.

Matters to this vault as the classical theory Weatherall and Eleanor March's 2026 paper generalizes to the "natural equation" setting of general relativity, where it anchors their results on when a minimally-coupled natural equation's causal cones must coincide exactly with the spacetime metric's light cones, and on what conservation properties fall out of naturality alone.

References

• 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