Emergent 1/r² Gravity from Vortical Energy Densities: An AI-Assisted Computational Proof of Concept

This paper presents a computational model investigating the emergence of gravitational-like forces from the dynamics of vortical solitons within a nonlinear field. By modeling energy density using the Nonlinear Schrödinger Equation (NLS) and emulating a 3D spatial response via a 3D Green's kernel in Fourier space, we demonstrate that the static force between two vortices decays precisely as 1/r². The numerical simulation was developed under human scientific direction, utilizing advanced AI-assisted coding to handle the mathematical execution. The results yield a measured exponent of n = -2.0577. Furthermore, we demonstrate that the orbital motion of these vortices generates propagating perturbations in the energy field, offering a computational analogue for gravitational wave emission. These findings provide a proof of concept that both static and dynamic macroscopic gravitational phenomena can emerge dynamically from microscopic energy distributions without being explicitly programmed into the field equations.