Strong gravitational lensing from compact bodies: analytical results

TL;DR

This paper introduces a non-perturbative analytical method for calculating light deflection angles in static, spherically symmetric spacetimes, improving accuracy over previous methods and verified across various metrics.

Contribution

The authors develop a new analytical approach that accurately describes gravitational lensing by compact bodies, including the photon sphere, with minimal error.

Findings

Error less than 0.5% across all regimes

More accurate than previous methods

Provides analytical expressions for deflection angles

Abstract

We develop a non--perturbative method that yields analytical expressions for the deflection angle of light in a general static and spherically symmetric metric. It is an improvement on a method previously devised by the authors, and provides a correct description of the photon sphere already to first order. We also propose an alternative approach that provides general simpler formulas, although with larger errors. We apply our technique to different metrics and verify that the error is at most $0.5 %$ for {\sl all} regimes. We show that our approximation is more accurate than others proposed earlier.