Calculating N-Body Dynamics Without Force-Based Gravity: Motion via Manifold Stretching Gradients

This proposes a novel geometric interpretation of the N-body problem by mapping the trajectories of interacting bodies onto a differentiable NURBS manifold. By shifting the focus from classical Newtonian force vectors to the intrinsic properties of the manifold—such as the local metric tensor and principal curvatures—the research identifies a profound coupling between the manifold and physical variables like velocity and gravitational potential. Specifically, the paper demonstrates that gravitational interaction manifests as geometric "bays" or troughs, where motion is driven by the stretching gradients of the manifold, suggesting that gravity itself may be an emergent property of the manifold's local area scaling.