Gravitational lensing in the Kerr-Randers optical geometry

TL;DR

This paper introduces a novel geometric approach using Finsler-Randers optical geometry and the Gauss-Bonnet theorem to analytically compute light deflection in Kerr spacetime, enhancing understanding of gravitational lensing.

Contribution

It presents a new method combining Finsler geometry and the Gauss-Bonnet theorem to determine gravitational lensing deflection angles in Kerr spacetime.

Findings

Explicit calculation of the leading terms of the deflection angle.

Application of the Gauss-Bonnet theorem to Finsler geometry.

Enhanced analytical understanding of gravitational lensing in rotating black holes.

Abstract

A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a suitable osculating Riemannian manifold, adapted from a construction by Naz\i m, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.