Gravitational Lensing Under the Effect of Weyl and Bumblebee Gravities: Applications of Gauss-Bonnet Theorem

Understand

In this paper, we use the Gauss Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation.

• To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss-Bonnet theorem, which is first done by Gibbons and Werner.
• Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as compared with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee gravity.
• Moreover, we investigate the deflection angle by Einstein-Rosen type wormhole in Weyl gravity and in bumblebee gravity.