Null Congruence Stability and Spectral Structure in Effective Higher-Dimensional Gravity

We develop a linearized stability analysis of null congruence dynamics near marginal focusing by introducing a causal stress-energy response sector while preserving the instantaneous Einstein constraint. The resulting second-order structure emerges only in regimes where a restorative feedback coefficient (κ > 0) is generated by specified stress closures (e.g., dissipative or semiclassical contributions) and does not represent generic vacuum general relativity. The framework is extended within the Shiromizu–Maeda–Sasaki effective formalism to incorporate higher-dimensional degrees of freedom. Schur complement analysis shows that bulk-induced spectral shifts enter at second order in the coupling, maintaining perturbative consistency with current four-dimensional gravitational-wave constraints. The analysis is intended as a controlled effective-theory investigation of null congruence stability under dynamical stress-response assumptions.