Simulating Gravitational Dynamics via Scalar Field Propagation

Brendan Toupin^*

• DIRECTV LLC, El Segundo, United States

We present a deterministic scalar-field propagation framework in which structured transport R(x) (symmetric positive-definite) and damping Lambda(x) generate reproducible media analogs of gravitational-like behavior. With the source term off (S = 0), dynamics arise purely from initial conditions under d2Phi/dt2 − div( R(x) * grad Phi ) + Lambda(x) * dPhi/dt = 0. The suite demonstrates deflection and ray bending, transit delay with escape thresholds, collapse/trapping and orbital containment, anisotropy-induced drift, repulsion via curvature inversion, and phase-sensitive interference. Each phenomenon is stated as a primary metric with an explicit falsifier and verified by energy-budget closure (Rayleigh loss + boundary flux) within 1–3% after transients, alongside spectral-safety and robustness checks. The framework yields concrete predictions: bend angle scales with grad R and flips sign under gradient reversal; transit delay grows monotonically with the path integral of Lambda and can prevent exit; bounded orbits satisfy r_min <= r(t) <= r_max over a finite capture band; the radial drift in a radial R profile follows |dr/dt| ∝ r^(−alpha) with alpha ≈ 2; transverse drift sign matches the sign of the off-diagonal/tilt in R; and interference visibility follows a cosine law in relative phase. Null and negative controls (uniform R, Lambda = 0, gradient reversal) are included. Numerically, we use stability-respecting discretizations and record discrete energies, loss, and boundary flux each step. Main figures use 256x256 grids; representative 512x512 confirmations for deflection and containment reproduce primary metrics and are included in the supplement. All code, configs, and outputs needed to regenerate figures are archived (versioned DOIs), supporting end-to-end transparency and reuse. The claims are explicitly operational—transport and loss in structured media—not statements about mass or spacetime curvature. Our contribution is twofold. First, we show that thirteen gravity-like kinematics (e.g., bending, orbital containment, transit delay) arise from a single, unified scalar transport law with spatially varying resistance and damping, d2Phi/dt2 − div( R(x) * grad Phi ) + Lambda(x) * dPhi/dt = 0. Second, we codify each phenomenon as an experiment with observables, acceptance gates, and falsification routes, and we release a complete reproducibility bundle. We emphasize these are operational analogs—not claims about spacetime curvature.