Gravitational Waves and Lensing as Fabric Deformations: A Unified Test of Al-Ani Fabric Theory

Gravitational waves and gravitational lensing are typically treated as independent phenomena within general relativity. In Al-Ani Fabric Theory, they emerge as two manifestations of the same underlying entity: deformations of the spacetime fabric. From the fundamental dynamical equation ∂δ/∂t = D∇²δ - Γδ + S, we derive both the wave equation for propagating deformations (gravitational waves) and the static deformation field responsible for light deflection (gravitational lensing). The theory predicts specific modifications to both phenomena compared to general relativity, governed by the same two fundamental parameters D and Γ (or equivalently λ = √(D/Γ) and τ = 1/Γ). Key predictions include: • Amplitude-dependent dispersion in gravitational waves (Δv/c ∼ 10⁻⁵), testable with LIGO/Virgo • Suppressed Einstein radii for galaxy-scale lenses (7 ± 2% for M ∼ 10¹² M⊙), testable with Euclid • Modified time delays (3 ± 1% deviation from GR), testable with Roman Space Telescope • High-frequency suppression for LISA sources (f_c ∼ 10⁻⁴ Hz) The theory is falsifiable: if λ measured from GW dispersion differs from λ measured from lensing suppression by more than 2σ, the theory must be abandoned. This paper is part of the Al-Ani Fabric Theory series (12 papers, all on Zenodo), which unifies 40+ physical phenomena with a single dynamical equation and only two fundamental parameters.