Theoretical gravitational lensing. Beyond the weak-field small-angle approximation

TL;DR

This paper reviews advanced theoretical gravitational lensing methods that do not rely on weak-field or small-angle approximations, covering analytical and qualitative approaches in various spacetime geometries.

Contribution

It provides a comprehensive overview of exact and qualitative methods for gravitational lensing beyond common approximations, including integrable spacetimes and topological techniques.

Findings

Analytical solutions for light rays in spherically symmetric and Kerr spacetimes.

Qualitative insights into lensing properties using Morse theory and bifurcation analysis.

Extension of lensing theory to strong-field regimes without small-angle assumptions.

Abstract

An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted to analytical methods considering spacetimes in which the equations for light rays (lightlike geodesics) is completely integrable. This includes spherically symmetric static spacetimes, the Kerr spacetime and plane gravitational waves. The second part is devoted to qualitative methods which give some information on lensing properties without actually solving the equation for lightlike geodesics. This includes Morse theory, methods from differential topology and bifurcation theory.