On Spectral Structure in a Non-Separable Rotating Geometry: Normal Modes and Holographic Response in the Rotating AdS-Teo Wormhole

Abstract

Rotating traversable wormholes provide a horizonless setting in which to investigate wave dynamics beyond the separable structures familiar from black-hole perturbation theory. We study scalar perturbations in the rotating AdS-Teo wormhole and show that the absence of separability naturally leads to a coupled-channel formulation in which the angular harmonic modes interact through a matrix-valued Sturm-Liouville operator. Imposing regularity at the wormhole throat together with asymptotically anti-de Sitter boundary conditions yields a determinant quantization condition that determines a discrete normal-mode spectrum. A controlled two-channel truncation illustrates how angular-channel mixing produces frequency shifts, spectral repulsion, and collective mode reorganization. From the asymptotic solutions, we construct a matrix-valued boundary response function whose poles coincide with the bulk normal-mode frequencies, while its off-diagonal components provide a direct signature of rotation-induced channel mixing. We further investigate the renormalized vacuum polarization, whose interference terms reveal local quantum signatures of non-separability, and examine semiclassical geodesic correlators as complementary probes of two-boundary connectivity. These results suggest that coupled-channel spectral theory provides a natural organizing principle for rotating, non-separable geometries, replacing conventional mode separability with a framework based on collective normal modes, matrix-valued response functions, and coupled quantum observables.