The gravitational lensing effect at higher order under weak-field approximation is believed to be important to distinguish black holes and other compact objects such as wormholes. The deflection angle of a generic wormhole is difficult to solve analytically; thus approximation methods are implemented. In this paper, we investigate the weak-field deflection angle of a specific wormhole, the Ellis-Bronnikov wormhole, up to the $1/b^4$ order. We use different approximation formalisms, study their precision at $1/b^4$ order by a comparison to a purely numerical result, and finally rank these formalisms by their accuracy. Moreover, we find that certain formalisms are sensitive to the choice of coordinate system; thus it is important to choose the coordinate system appropriately for the evaluating of lensing physics.

• Received 6 April 2023
• Revised 9 June 2023
• Accepted 15 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.023004