IndisputableMonolith.Relativity.Geodesics.NullGeodesic
The NullGeodesic module defines null geodesics as curves with zero interval using affine parameter lam, together with supporting objects such as InitialConditions and lemmas on straight lines in Minkowski space. Researchers modeling light-like propagation within the Recognition Science relativity framework would cite these results. The module aggregates definitions and basic lemmas imported from Geometry and Calculus with no internal complex proofs.
claimA null geodesic is a curve $x^mu(lambda)$ satisfying $ds^2=0$ with affine parameter $lambda$.
background
This module sits in the Relativity.Geodesics namespace of the Recognition Science framework and imports the Calculus module (a Calculus Module Aggregator) together with the Geometry module (which re-exports all geometry components). The module DOC_COMMENT states that a null geodesic is a path with zero interval using lam for the affine parameter. Sibling declarations cover NullGeodesic, InitialConditions, straight_null_geodesic, null_geodesic_exists_minkowski, affine_reparametrization, minkowski_straight_line_is_geodesic and geodesic_unique.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module supplies the core definitions and Minkowski-space lemmas for null geodesics that underpin further geodesic analysis in the Relativity section. It fills the definitional step for light-like paths in the Recognition Science derivation, consistent with the overall forcing chain and geometry tools imported from upstream modules. No specific downstream theorems are listed in the current dependency graph.
scope and limits
- Does not derive the geodesic equation from the Recognition Composition Law.
- Does not treat timelike or spacelike geodesics.
- Does not address curved spacetimes beyond Minkowski examples.
- Does not include numerical or simulation implementations.