Strong deflection limit analysis and gravitational lensing of an Ellis wormhole

TL;DR

This paper extends a method for calculating gravitational lensing in strong fields to ultrastatic spacetimes, applying it to an Ellis wormhole to better understand lensing effects near such exotic objects.

Contribution

It introduces an improved method for strong deflection limit analysis applicable to ultrastatic spacetimes, specifically demonstrating it on an Ellis wormhole.

Findings

Derived a more accurate deflection angle formula for ultrastatic spacetimes.

Applied the method to an Ellis wormhole to analyze its gravitational lensing.

Discussed the error term in the deflection angle approximation.

Abstract

Observations of gravitational lenses in strong gravitational fields give us a clue to understanding dark compact objects. In this paper, we extend a method to obtain a deflection angle in a strong deflection limit provided by Bozza [Phys. Rev. D 66, 103001 (2002)] to apply to ultrastatic spacetimes. We also discuss on the order of an error term in the deflection angle. Using the improved method, we consider gravitational lensing by an Ellis wormhole, which is an ultrastatic wormhole of the Morris-Thorne class.