Simulating gravitational dynamics via scalar field propagation - Toupin, Brendan (Frontiers in Physics, 2025)
IntroductionWe study whether gravity-like kinematics (bending, time-delay, redshift-like shifts, capture/orbits) can arise as media analogs from a deterministic scalar-field propagation model without invoking mass or spacetime curvature.MethodsWe evolve a real scalar field under a spatially varying symmetric positive-definite transport tensor R(x) and non-negative damping field Λ(x); with source off (S≡0). Thirteen simulations quantify deflection, transit delay with escape thresholds, collapse/trapping and orbital containment, anisotropy-induced drift, repulsion under curvature inversion, and interference. We monitor energy budgets (Rayleigh loss + boundary flux) and check spectral safety and robustness.ResultsObservables are reproducible on 256 × 256 grids with 512 × 512 confirmations for key cases. Bending scales with ∥∇R∥ and flips sign under gradient reversal; transit delay increases monotonically with ∫Λdx and can prevent exit; bounded orbits satisfy a/p≤1.15 over a finite capture band; radial drift in 1/r2 profiles follows |r ̇|∝r^(-α) with a≈2; transverse drift sign matches sign(Rxy); interference visibility follows a cosine in relative phase.DiscussionResults constitute operational gravitational analogs—transport and loss in structured media—rather than statements about spacetime curvature. We release code/configs/outputs for full reproducibility and outline laboratory test paths.