IndisputableMonolith.Relativity.GW.TensorDecomposition
This module decomposes general spatial metric perturbations into transverse-traceless and remaining sectors on FRW backgrounds. Gravitational wave analysts cite it for the projection operators and uniqueness statements needed before action expansions. It aggregates definitions and lemmas drawn from the imported geometry and cosmology modules.
claimDecomposition of a spatial metric perturbation $h_{ij}$ into its transverse-traceless part $h_{ij}^{TT}$, vector, and scalar sectors via the projection operator $P_{ij}^{kl}$.
background
The module sits inside linearized gravity on Friedmann-Robertson-Walker spacetimes. It introduces TensorPerturbation as the general spatial metric perturbation and supplies decompose_perturbation together with projection_operator_TT and decomposition_unique. Upstream, the Geometry module re-exports all geometry components for convenient importing, while FRWMetric supplies the cosmological background metric.
proof idea
This is a definition module, no proofs. It collects the sibling declarations TensorPerturbation, decompose_perturbation, projection_operator_TT, decomposition_unique, and decomposition_unique_holds.
why it matters in Recognition Science
Supplies the TT gauge decomposition $h_{ij}^{TT}$ required by the parent GW module for tensor perturbation theory. The GW module uses it to build the quadratic action in ActionExpansion and to derive propagation speed and GW170817 constraints.
scope and limits
- Does not derive the wave equation satisfied by tensor modes.
- Does not compute the quadratic action expansion.
- Does not evaluate propagation speed corrections.
- Does not incorporate observational bounds from GW170817.