IndisputableMonolith.Relativity.Geodesics.NullGeodesic
The NullGeodesic module defines null geodesics as curves with vanishing spacetime interval using an affine parameter lam. It supplies initial conditions, straight-line constructions in Minkowski space, and basic uniqueness results. The module aggregates these elements from its geometry and calculus imports to support light-like path analysis in the relativity component of Recognition Science.
claimA null geodesic is a curve $γ(λ)$ satisfying $g(γ̇,γ̇)=0$ where $λ$ is the affine parameter and the interval vanishes identically.
background
The module sits in the Relativity domain and imports the Geometry aggregator, which re-exports all geometry components for convenient use, together with the Calculus aggregator. Its central definition is the null geodesic: a path with zero interval parameterized by lam. This supplies the local setting for subsequent sibling declarations on initial conditions, straight null geodesics in Minkowski space, affine reparametrization, and uniqueness.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the core object for null geodesics that feeds sibling results on existence in Minkowski space and geodesic uniqueness. It contributes to the Recognition Science treatment of light-like trajectories within the broader relativity formalization.
scope and limits
- Does not address timelike or spacelike geodesics.
- Does not treat curved spacetime metrics beyond Minkowski.