Gravitational lensing by rotating wormholes

In this paper the deflection angle of light by a rotating Teo wormhole spacetime is calculated in the weak limit approximation. We mainly focus on the weak deflection angle by revealing the gravitational lensing as a partially global topological effect. We apply the Gauss-Bonnet theorem (GBT) to the optical geometry osculating the Teo-Randers wormhole optical geometry to calculate the deflection angle. Furthermore we find the same result using the standard geodesic method. We have found that the deflection angle can be written as a sum of two terms, namely the first term is proportional to the throat of the wormhole and depends entirely on the geometry, while the second term is proportional to the spin angular momentum parameter of the wormhole. A direct observation using lensing can shed light and potentially test the nature of rotating wormholes by comparing with the black holes systems.