Strong field limit of black hole gravitational lensing

TL;DR

This paper develops an analytical theory for gravitational lensing in the strong field limit of Schwarzschild black holes, providing formulas for critical curves, images, and magnifications with high accuracy.

Contribution

It introduces a new analytical framework for strong field gravitational lensing, extending the weak field approach to black holes with precise mathematical expressions.

Findings

Derived formulas for critical curves and relativistic images

Achieved high-accuracy descriptions of lensing phenomena in strong fields

Provided a foundation for further observational and theoretical studies

Abstract

We give the formulation of the gravitational lensing theory in the strong field limit for a Schwarzschild black hole as a counterpart to the weak field approach. It is possible to expand the full black hole lens equation to work a simple analytical theory that describes at a high accuracy degree the physics in the strong field limit. In this way, we derive compact and reliable mathematical formulae for the position of additional critical curves, relativistic images and their magnification, arising in this limit.