# Higher-order correction to weak-field lensing of an Ellis-Bronnikov wormhole

## TL;DR

This paper calculates higher-order weak-field gravitational lensing effects for the Ellis-Bronnikov wormhole, comparing approximation methods to numerical results to improve understanding of wormhole lensing signatures.

## Contribution

It introduces a detailed analysis of higher-order deflection angles for the Ellis-Bronnikov wormhole using multiple approximation formalisms and assesses their accuracy against numerical solutions.

## Key findings

- Certain approximation formalisms are more accurate at 1/b^4 order.
- Coordinate system choice significantly affects lensing calculations.
- Higher-order corrections improve wormhole lensing modeling.

## Abstract

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.