Deflection angle of light in an Ellis wormhole geometry

TL;DR

This paper analyzes the deflection angle of light in an Ellis wormhole spacetime, deriving exact and asymptotic expressions, and clarifies the limitations of previous approximations due to the wormhole's topology.

Contribution

It provides a complete elliptic integral expression for the light deflection angle and highlights the breakdown of previous approximations at higher orders.

Findings

Exact deflection angle expressed via elliptic integral

Asymptotic expressions in weak field limit derived

Previous simple approximations are invalid beyond leading order

Abstract

We reexamine the light deflection by an Ellis wormhole. The bending angle as a function of the ratio between the impact parameter and the throat radius of the wormhole is obtained in terms of a complete elliptic integral of the first kind. This result immediately yields asymptotic expressions in the weak field approximation. It is shown that an expression for the deflection angle derived (and used) in recent papers is valid at the leading order but it breaks down at the next order because of the nontrivial spacetime topology.