IndisputableMonolith.Relativity.Compact.StaticSpherical
The StaticSpherical module supplies the explicit Schwarzschild metric for vacuum static spherical symmetry with nonzero mass. Compact-object and lensing researchers cite it when modeling horizons or shadow fringes. It is a pure definition module that assembles the metric functions f(r) and g(r) from imported geometry and fields without any proofs.
claimThe Schwarzschild metric takes the form $ds^2 = -f(r)dt^2 + g(r)dr^2 + r^2 dΩ^2$ with $f(r) = 1 - 2M/r$ and $g(r) = (1 - 2M/r)^{-1}$ for $r > 2|M|$, extended by a positive constant inside the coordinate singularity.
background
This module aggregates definitions inside the Relativity section of Recognition Science. It imports the Geometry, Calculus, and Fields aggregators to supply the metric components StaticSphericalMetric and SchwarzschildMetric. The setting is vacuum static spherical symmetry (M ≠ 0, ρ = 0, ψ = 0) with the standard spherical line element and the eight-tick octave structure inherited from the parent framework.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
It supplies the metric used by the Compact module to derive Bekenstein-Hawking entropy from ledger capacity and by Lensing.ShadowPredictions to formalize the 8-tick cycle phase-fringe effect at the event horizon.
scope and limits
- Does not derive the metric from the Recognition Composition Law.
- Does not treat rotating or dynamic solutions.
- Does not compute numerical shadow sizes or entropy values.
- Does not incorporate quantum or higher-order corrections.