Non-Newtonian Galactic Dynamics: An Interactive N-Body Simulation and Logarithmic Spacetime Potential Model for Flat Rotation Curves

Standard Newtonian dynamics coupled with visible baryonic mass distributions fail to account for the observed flat rotational velocity curves of spiral galaxies, traditionally necessitating the postulation of non-baryonic dark matter halos. In this work, we propose an alternative phenomenological framework based on an informational spacetime deformation model. By replacing the classical point-mass gravitational potential with a composite model comprising a Newtonian core ($\Phi_{Newton} \propto -1/r$) and an emergent logarithmic information potential ($\Phi_{Info} \propto \ln(r)$), we derive an analytical acceleration field that naturally produces flat asymptotic rotation profiles. We introduce a real-time, highly optimized symplectic N-body simulation tool ($N=2500$) integrated with dynamic spacetime mesh topology and statistical 1-sigma dispersion analysis. The computational results demonstrate that varying the informational coupling constant $K_{info}$ successfully scales the outer galactic velocity dispersion without invoking hidden mass parameters.