Scalar-Field Wave Dynamics and Quasinormal Modes of the Teo Rotating Wormhole

Abstract: We analyze scalar field perturbations of the rotating Teo wormhole and compute its quasinormal mode (QNM) spectrum using WKB methods in a fully horizonless geometry. The Klein Gordon equation separates and yields a Schrödinger type radial equation with a single, smooth potential barrier shaped by the localized frame dragging profile of the wormhole throat. This barrier supports damped oscillatory modes across the full spin range examined. The resulting QNM spectrum exhibits a coherent and monotonic dependence on rotation. As the spin increases, both the oscillation frequency and the damping rate decrease, indicating progressively longer-lived modes in the absence of horizon induced absorption. In the eikonal limit, we extract the photon-ring radius, orbital frequency, and Lyapunov exponent, and verify the standard QNM-Eikonal correspondence. Comparison with Kerr black holes reveals qualitative differences. Whereas Kerr QNMs are governed by horizon absorption and exhibit symmetric prograde/retrograde mode splitting, the Teo wormhole displays a stronger but spatially confined spin response, partial reflection at the throat, and a distinctive one-sided splitting that saturates rapidly with increasing spin. Although the rotating Teo wormhole admits an ergoregion and superradiant compatible frequency kinematics, the absence of an event horizon or dissipative boundary prevents classical superradiant amplification. These results demonstrate how rotation and boundary conditions jointly shape wave propagation in horizonless compact objects and provide characteristic spectral signatures distinguishing rotating wormholes from Kerr black holes.