Lensing Suppression in Finite‑Response Coupled Field Dynamics (FRCFD)

Lensing Suppression in Finite‑Response Coupled Field Dynamics (FRCFD)

Lensing Suppression in Finite‑Response Coupled Field Dynamics (FRCFD)

March 2026

I. Introduction

In General Relativity (GR), gravitational lensing arises from curvature of a four-dimensional spacetime manifold. In Finite‑Response Coupled Field Dynamics (FRCFD), lensing emerges from gradients in substrate impedance encoded by the substrate field S(r). Because the substrate possesses a finite maximum response capacity, the deflection of null trajectories is intrinsically bounded.

This bounded response produces measurable deviations from GR in the strong-field regime, characterized by the Lensing Suppression Factor η(b), which serves as the primary quantitative signature of a finite-response substrate.

II. Null Propagation in a Finite‑Response Substrate

The emergent metric in FRCFD is determined by the coarse-grained substrate field Φ(r):

ds² = - c² e^(2 Φ/Φ_max) dt² + e^(2 Φ/Φ_max) (dr² + r² dΩ²)

For null geodesics (ds² = 0), the propagation speed and trajectory curvature depend on the radial profile Φ(r), which is determined by the substrate equation:

∂²S/∂t² - c² ∇²S + β S³ = F_R(S | Ψ)

In static, spherically symmetric configurations S = S(r), the dual‑channel coupling operator is:

F_R(S | Ψ) = T[Ψ] · exp(-T[Ψ]/T_max) · exp(-S/S_max)

This operator enforces saturation as S → S_max or T[Ψ] → T_max. The finite-response structure determines the deviation from GR.

III. Lensing Suppression Formalism

Let α_GR(b) denote the GR deflection angle for a null trajectory with impact parameter b around a compact mass M. Let α_FRCFD(b) denote the corresponding deflection angle computed from the emergent metric:

α_FRCFD(b) = α_GR(b) · [1 - η(b)]

The Lensing Suppression Factor η(b) satisfies:

  • Weak-field correspondence: lim_{b → ∞} η(b) = 0, recovering the Einstein deflection: α_GR(b) = 4GM / (c² b).
  • Strong-field saturation: S(r) → S_max ⇒ η(b) → η_max < 1.
  • Regularity at the photon sphere: Because F_R saturates, the substrate cannot generate unbounded curvature: α_FRCFD(b) < α_GR(b) for b ≈ r_s.

IV. Event Horizon Telescope Predictions

Finite substrate response modifies observable shadow morphology:

  • Increased Shadow Diameter: The effective photon orbit radius exceeds the GR prediction.
  • Diffuse Inner Boundary: The shadow edge is less sharply defined due to bounded curvature.
  • Finite‑Curvature Plateau: The photon sphere becomes a stable plateau rather than a divergent orbit.

These effects are testable in EHT observations of Sgr A* and M87*.

V. Conclusion

The Lensing Suppression Factor η(b) establishes FRCFD as a predictive field theory with falsifiable consequences. By defining gravitational behavior through finite‑response substrate dynamics, the framework provides a non-singular alternative to geometric curvature models, suitable for testing in extreme astrophysical environments.

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