On the Stability of Curvature-Induced Neutrino Splitting under Small Mass Perturbations

We investigate the stability of curvature-induced splitting for solutions of a first-order hyperbolic system arising from the Dirac equation in a curved space-time background. The system governs the evolution of a four-component field and incorporates geometric effects through variable coefficients determined by the underlying metric. In the massless case, the operator exhibits a structural decomposition that leads to a natural splitting of solutions into distinct propagation modes. We study whether this phenomenon per- sists under physically relevant perturbations, namely the introduction of a small mass and weak spatial variation of the geometry. We develop an operator-level perturbative framework that allows us to analyze the interaction between the resulting modes. We prove that the splitting structure remains stable under small perturbations and estab- lish a quantitative estimate showing that the interaction between modes is bounded by a quantity of order O (m + ε), where m is the mass parameter and ε characterizes the variation of the geometric coefficients. Explicit examples and numerical simulations are presented to illustrate both the persistence of the splitting mechanism and the emergence of higher-order corrections. The results demonstrate that curvature-induced splitting is a robust feature of the system and provide a bridge between idealized massless models and physically relevant regimes.