Gravitational lensing and deflection angles of generalised Ellis-Bronnikov wormhole embedded in a warped braneworld background

Abstract

We investigate null trajectories, deflection angles, and gravitational lensing in the spacetime of generalized Ellis-Bronnikov (GEB) wormholes and their embedding in a five-dimensional warped braneworld background (WGEB). The GEB geometry extends the standard Ellis-Bronnikov (EB) wormhole by introducing a steepness parameter $m \geq 2$, which controls the shape of the wormhole throat while partially improving on the violation of classical energy conditions. We compare the lensing properties of the four-dimensional GEB geometry with those of its warped five-dimensional counterpart, where the effect of the extra dimension is encoded through the parameter $\delta$, associated with the photon momentum along the extra dimension. Analytic expressions for the deflection angle are obtained in both weak and strong-lensing regimes, and the known EB results are recovered for $m = 2$. For $m > 2$, analytic approximation and numerical analysis is used where exact analytic solutions are not available. We show that the parameter $m$ leaves clear and distinguishable signatures in the deflection angle, Einstein ring radius, and image positions, while the presence of the warped extra dimension modifies the effective impact parameter and leads to a broadening of the photon sphere and lensed images.