Dark Matter Induced by Gravitational Potential: MOND-like Phenomenology at Galactic Scales

The Gravitational Potential Response Framework (GPRF) Dark Matter Induced by Gravitational Potential: MOND-like Phenomenology at Galactic Scales Rotation Curves, the Baryonic Tully-Fisher Relation, and the Outer Halo Cutoff James Richard Marsen | Independent Researcher | ORCID: 0009-0004-5112-0181 This work presents the Gravitational Potential Response Framework (GPRF), a structural approach to galactic dynamics that recovers the empirical successes of both dark matter and Modified Newtonian Dynamics — flat rotation curves, the tight mass-velocity correlation observed across all spiral galaxies, and the finite boundary of the galactic halo — from a single linear constitutive relation and one coupling parameter, without new particles, modified gravity, or ad hoc assumptions. The MOND formula emerges as a mathematical consequence rather than a starting assumption. The constitutive relation rhoₙb = ξ δφ combined with the standard Newtonian operator and classical potential theory yields an augmented Poisson equation whose Yukawa exterior solution produces a broad velocity plateau and a structural halo cutoff. The sign of the screening term is provisionally adopted as a postulate for physical viability, pending its derivation in the follow-up program. The induction parameter is normalized per galaxy to the baryonic Tully-Fisher relation via k² = a₀/ (GMb), taking one empirical scale a₀ through one normalization condition; this recovers the correct BTFR slope and a specific radial acceleration relation. For the Milky Way this normalization gives k⁻¹ ≈ 14 kpc, consistent with the Keplerian decline recently revealed by Gaia DR3 (Jiao et al. 2023; Ou et al. 2024) as a self-consistency check rather than an independent prediction. Because the cutoff scale varies with galaxy mass as k⁻¹ ∝ v²flat/a₀, the framework predicts a specific, falsifiable pattern: halo cutoffs appear at progressively larger radii in lower-mass galaxies. Key results: MOND-like 1/r scaling at intermediate radii emerges as a structural consequence, not an assumption Outer halo cutoff at k⁻¹ ≈ 14 kpc, consistent with Gaia DR3 without rotation-curve fitting Three-regime mass structure: dwarfs (interior-dominated), MW-mass (cutoff visible), massive spirals (cutoff beyond survey reach) — explains the absence of declines in SPARC Implied radial acceleration relation derived analytically from the exterior solution Sign of the screening term adopted as a postulate; derivation from global self-consistency is the central open problem of GPRF II Submitted to European Physical Journal Plus (EPJ Plus). Preprint DOI: https: //doi. org/10. 5281/zenodo. 20450130