>[!warning] >This content has not been peer reviewed. # RST Lensing — Refraction Illustration The disformal term $(e^{2q}-e^{-2q}) A_\mu A_\nu$ acts as a **refractive index** for the substrate: where workload $q$ is high, the effective propagation is restricted and light is deflected. This note describes the calculation that illustrates lensing as bandwidth congestion. **Mechanism:** [[RST Lensing (Disformal)]]. The **derived** (Baseline 1.7) physical metric for photons is $\tilde{g}_{\mu\nu} = e^{2q}g_{\mu\nu} - (e^{2q}-e^{-2q})A_\mu A_\nu$ (Refraction Identity). The deflection we measure in clusters is the substrate's update-lag — no dark matter required. For a galaxy-cluster lensing calculation using the bending boost, see [[RST Refractive Lensing - Code]]. Results: [[RST Lensing Results]]. --- ## Calculation logic - **Inputs:** Impact parameter $r$; workload $q(r)$ (e.g. $q \propto 1/r$ in weak field); disformal strength $\beta$ (illustrative). - **GR deflection:** $\alpha_{\text{GR}} \propto 1/r$. - **RST correction:** Refractive factor $1 + \beta q$; $\alpha_{\text{RST}} = \alpha_{\text{GR}} \times (1 + \beta q)$. - **Output:** Deflection vs $r$ (GR vs RST). See [[RST Lensing Results]]. ## Interpretation - **GR:** Deflection ∝ 1/r (from mass). - **RST:** Deflection = (1 + β·q) × GR term. Where the substrate is busy maintaining mass (high $q$), the refractive index increases and light bends more. No dark matter halo is invoked; the "extra" bending is the substrate's **information congestion**.