Frame-dragging and light deflection in rotating optical wormhole spacetimes

In this work, we present a detailed analytical study of null geodesics in a family of rotating optical wormhole spacetimes with constant negative Gaussian curvature, encompassing hyperbolic, elliptic, and Beltrami geometries. By explicitly deriving the full set of null geodesic equations, we characterize photon trajectories in these curved, rotating backgrounds. Our analysis highlights the role of rotation in shaping light paths, showing how frame-dragging effects, ergoregion emergence (despite the absence of event horizons), and alterations in causal structure influence photon dynamics. We construct exact forms of the effective potential governing radial photon motion, allowing for a systematic investigation of orbit stability and critical trajectories. Closed-form expressions for gravitational deflection angles are obtained, along with clear conditions for the presence and positioning of optical horizons unique to these geometries. Our findings demonstrate that the interplay between rotational effects and the geometry-specific radial shape functions crucially determines how light behaves in these exotic spacetimes. While some features echo those of analog gravity models, our framework remains strictly within general relativity. This study provides a rigorous foundation for understanding gravitational lensing and horizon behavior in spacetimes with nontrivial topology.