---
title: "Symmetric hyperbolic system"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Symmetric hyperbolic system"
aliases: []
first_seen: "2026-10-30T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["well-posed initial-value problem","Kurt Otto Friedrichs","natural equation","general relativity","causal structure"]
seek_code_commit: "d40ee39"
---


The standard framework, originated by [[entity-kurt-otto-friedrichs|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 [[entity-james-owen-weatherall|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]]