A Mathematical Model of Stellar Trajectories Using the Kuznetsov Tensor to Describe Motion Evolution on a Galactic Scale

This paper presents a new mathematical framework for describing stellar pathways in the Galaxy based on the Kuznetsov tensor, a geometric–physical construct for modeling systems with singularities and complex curvature evolution. Traditional models rely on Newtonian gravity, relativistic metrics, or N-body simulations, but they inadequately capture discontinuous curvature zones, anisotropic gravitational fluctuations, and topological transitions. The proposed approach introduces a tensor field Kij that characterizes local and global singularities influencing stellar trajectories. The model defines a modified metric evolution equation analogous to a generalized Ricci flow, augmented with a singularity-driving term governed by the Kuznetsov tensor. This enables refined description of star–galaxy interactions, detection of critical curvature corridors, and prediction of pathway branching, stability domains, and large-scale reconfiguration. The framework can be applied to spiral-arm evolution, exoplanet migration, interstellar transfer routes, and engineered stellar navigation systems. Overall, the Kuznetsov tensor provides a mathematically consistent and physically insightful tool for modeling star-route dynamics in singular, evolving gravitational geometries.