Deflection angle of photon through dark matter by black holes and wormholes using the Gauss-Bonnet theorem

Abstract: In this research, we use the Gibbons-Werner method (Gauss-Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of the weak gravitational lensing within the Maxwell's fish eye-like profile and dark matter medium. The angle is seen as a partially topological effect and the Gibbons-Werner method can be used on any asymptotically flat Riemannian optical geometry of compact objects in dark matter medium.