Weak deflection angle of black-bounce traversable wormholes using Gauss-Bonnet theorem in the dark matter medium

TL;DR

This paper calculates the weak deflection angle of light around black-bounce traversable wormholes using the Gauss-Bonnet theorem, considering the influence of dark matter medium and bounce parameter effects.

Contribution

It introduces a novel application of the Gauss-Bonnet theorem to evaluate light deflection in wormhole spacetimes with dark matter effects.

Findings

Weak deflection angle depends on the bounce parameter a.

Dark matter medium influences the light bending angle.

Gauss-Bonnet theorem reveals light bending as a topological effect.

Abstract

In this paper, we first use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.