Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime

TL;DR

This paper improves the analysis of gravitational lensing in strong deflection limits for a broad class of static, spherically symmetric spacetimes, providing analytical formulas and emphasizing the importance of variable choice.

Contribution

It introduces an improved method for strong deflection limit analysis applicable to general asymptotically flat, static, spherically symmetric spacetimes, including ultrastatic cases.

Findings

Analytical deflection angle formulas for Reissner-Nordstrom spacetime.

Reexamination of Ellis wormhole deflection angle in strong limit.

Highlighting the significance of variable choice in the analysis.

Abstract

Gravitational lensing by the light sphere of compact objects like black holes and wormholes will give us information on the compact objects. In this paper, we provide an improved strong deflection limit analysis in a general asymptotically flat, static, spherically symmetric spacetime. The strong deflection limit analysis also works in ultrastatic spacetimes. As an example of an ultrastatic spacetime, we reexamine the deflection angle in the strong deflection limit in an Ellis wormhole spacetime. Using the strong deflection limit, we obtain the deflection angle analytically for the Reissner-Nordstrom spacetime. The point of the improvement is the definition of a standard variable in the strong deflection limit analysis. We show that the choice of the variable is as important as the choice of the coordinates and we conclude that one should choose a proper variable for a given spacetime.