τ-Gravitational Wave

A τ-gravitational wave (`V.D53`) is a propagating perturbation δΔ_k^{(n)} of the holonomy-gap elements satisfying the linearized τ-Einstein equation with vanishing matter source (T^mat_lin = 0). Its chart-shadow is the standard linearized GR plane-wave solution, propagating at speed c = L·H with two transverse-traceless polarizations.

Categorical invariant. Vacuum solutions of V.D52 (linearized τ-Einstein) on the holonomy-gap module; chart-shadow gives plane gravitational waves at speed c.

Primary registry anchor: V.D53

Supporting items: V.D52, V.D51

1. I.K0 — Universe Postulate
2. V.D51 — τ-Einstein equation R^H = κ_τ · T^mat
3. V.D52 — Linearized τ-Einstein equation R^H_lin = κ_τ · T^mat_lin + O(ε²)
4. V.D53 — τ-Gravitational wave — vacuum perturbation δΔ_k^{(n)} solving the linearized equation with T^mat_lin = 0

Lean modules referenced: TauLib.BookV.GravityField.LinearEinstein

Calibration anchor: PG-P01-neutron

Calibration chain:

1. linearized τ-Einstein on the holonomy-gap module
2. wave speed c = L · H from the τ-cascade
3. SI bridge via m_n anchor and τ-second cascade for strain / frequency units

Manuscript reference: manuscript-sources/book-05/part02/ch14-linear-tau-einstein.tex

Status: Formalized

Module: TauLib.BookV.GravityField.LinearEinstein

Lean kind: definition

Lean symbol: Tau.BookV.GravityField.GravitationalWaveInTauframework

Related glossary entries

• PG-L04-tau-einstein-equation τ-Einstein Equation
• PG-L05-tau-newton-gravity τ-Newton's Law of Gravity