Analytical formulas for gravitational lensing

TL;DR

This paper introduces a new analytical method to accurately compute light deflection angles in gravitational lensing by transforming integrals into rapidly converging series, applicable to various metrics.

Contribution

The paper presents a novel series expansion technique for deriving precise analytical formulas for gravitational lensing deflection angles, improving accuracy over existing methods.

Findings

First-order formulas for spherically symmetric metrics derived

Method tested successfully in four different cases

Achieves high accuracy with simple first-order approximations

Abstract

In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly convergent series and provides extremely accurate approximations already to first order. We have derived a general first order formula for a generic spherically symmetric static metric tensor and we have tested it in four different cases.