Gravitational lensing in the Kerr-Randers optical geometry

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.Comment: 7 pages, 1 figure. Accepted by Gen. Rel. Grav. Version 2: change of notation in sec.