A charged black string wormhole with disclinations: Ray and wave optics

Abstract

This study investigates the optical behavior of photon rays and scalar waves in a three-dimensional static Black String Charged Wormhole (BSCWH) spacetime featuring topological disclinations. By analyzing null geodesics and the scalar Helmholtz equation, we present a unified treatment of light and wave propagation in curved spacetime with geometric defects. The disclination parameter accounts for angular deficits due to topological defects, the wormhole parameter governs throat geometry, and the Neveu-Schwarz (NS) charge introduces a string-inspired field contribution. These factors jointly influence light bending, photon orbits, and scalar wave modes. Scalar wave propagation reduces to a Schrödinger-like equation with an effective potential, from which we derive a spatially and frequency-dependent effective refractive index.  We obtain a closed-form weak-field deflection angle in terms of the geometric parameters and the disclination, and demonstrate that the trivial redshift function inherent to the BSCWH geometry precludes the formation of a photon sphere, yielding instead a critical impact parameter set by the throat radius. In the wave-optics sector, we show that the effective potential diverges at the throat, enforcing total reflection of scalar waves and producing frequency-dependent phase shifts characteristic of a dispersive analogue-gravity medium. Our findings reveal how curvature, charge, and topological features modify optical signatures, with implications for gravitational lensing, analogue gravity experiments, and optical media design. This work highlights the role of string-inspired effects and spacetime defects in shaping wave dynamics near wormholes.