Energy-Density Gravity: A Scalar-Potential Toy Model Reproducing Schwarzschild Time Dilation

Can the gravitational time dilation predicted by General Relativity be reproduced in a simple, flat 3D space without invoking spacetime curvature? This paper constructs a scalar-potential model to investigate that question.We present a model in which gravitational time dilation and weak-field dynamics arise from gradients in local energy density. For a static, spherically-symmetric source, we derive a potential Φ(r)=GM/r that satisfies a Poisson-type equation. By postulating that the proper time interval scales with this potential, the model successfully reproduces the Schwarzschild time-dilation factor in the weak-field limit.Significantly, the model is fully falsifiable, making specific, testable predictions for strong-field astrophysical phenomena that differ from General Relativity. These deviations provide a clear observational pathway to validate or falsify the energy-density approach to gravity.This self-contained model was motivated by the Energy-Density Gravity (EDG) concept, which is developed as part of the broader Dynamic Present Theory (DPΦ) framework. The full foundational theory is detailed in a separate work (DOI: 10.5281/zenodo.17069890).