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

TL;DR

This paper applies the Gauss-Bonnet theorem to calculate photon deflection angles caused by black holes and wormholes in dark matter environments, extending gravitational lensing analysis to complex optical geometries.

Contribution

It introduces a novel application of the Gibbons-Werner method to optical geometries involving dark matter, black holes, and wormholes, expanding the scope of gravitational lensing calculations.

Findings

Deflection angles can be computed as topological effects.

Method applicable to asymptotically flat Riemannian geometries.

Extension to Maxwell's fish eye-like profiles and dark matter media.

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.