Strong gravitational lensing from compact bodies: analytical results

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.