Numerical Solutions of the Static Spherical Einstein–FST Coupled System: Screened, Galactic, and Strong-Field Regimes

This repository provides the complete Python implementation andnumerical results for solving the static, spherically symmetriccoupled Einstein–Fundamental Speed Theory (FST) system. Three complementary codes are included: 1. A comprehensive validation suite covering the coupling identity, PPN parameter, energy conditions, quintic EFT identity, screening mechanism, and analytic correction estimates. 2. A full nonlinear solver for the screened solar exterior and the galactic regime, reconstructing the metric coefficients A(r) and B(r) from the Einstein equations with the FST stress tensor. 3. A strong-field black-hole exterior solver operating in geometric units, covering the horizon neighbourhood, photon sphere, ISCO, and outer region for stellar-mass black holes, Sgr A*, and M87*. Key results: - The coupling identity beta_eff = |lambda| nu0^2 / (6 c1) is recovered to machine precision. - The quintic EFT identity is verified with rms residual ~1e-2. - In the screened solar exterior, metric deviations from Schwarzschild are below 1e-10. - In the galactic regime, relative metric deviations are below 1e-10 while the field profile transitions from ~0.03 to ~1e-5. - At the photon sphere of M87*, Sgr A*, and a stellar-mass black hole, the numerical metric deviations are of order 1e-14, matching the analytic estimate of ~1e-13 for M87* and confirming that FST predicts no observationally accessible strong-field deviations from GR with current or near-future instruments. All codes are self-contained, documented, and produce publication-quality figures together with machine-readable JSON reports.