Lorentz-violating and topological effects on gravitational lensing phenomena and wave optics in wormhole backgrounds

Abstract

In this paper, we present a comprehensive analysis of photon trajectories and electromagnetic wave propagation in Lorentz-violating wormhole (LVWH) spacetimes embedded with topological defects-specifically, a cosmic string (CS) and a global monopole. We begin by deriving the equations of motion for null geodesics and analyze the behavior of photon paths in relation to the wormhole throat radius and parameters characterizing Lorentz symmetry violation. An explicit expression for the photon deflection angle is obtained, which is then used to derive a lens equation. We show that both the cosmic string parameter and Lorentz-violating terms significantly modify this equation compared to the standard Ellis–Bronnikov–Morris–Thorne wormhole (EBMTWH) case. To go beyond the geometric optics approximation, we formulate the scalar Helmholtz wave equation in the curved LVWH background. The resulting effective potential governing wave propagation is shown to be strongly dependent on the throat size, cosmic string parameter, and Lorentz-violating contributions. This leads to a spatially varying refractive index, indicating substantial alterations in the optical properties of the spacetime due to these effects. We extend the analysis to a second LVWH scenario embedded with a global monopole charge. A parallel treatment reveals how the interplay between the monopole parameter, throat radius, and Lorentz-violating terms influences both the lens equation and wave propagation characteristics. Our results highlight how topological defects combined with Lorentz symmetry breaking lead to distinctive modifications in both ray and wave optics, offering potential observational signatures and deeper insights into exotic gravitational structures.