Deflection Angle of Photons through Dark Matter by Black Holes and Wormholes Using Gauss-Bonnet Theorem

In this research, we used the Gibbons-Werner method (Gauss-Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of 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 a dark-matter medium.