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 Nazım, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.

7 pages, 1 figure. Accepted by Gen. Rel. Grav. Version 2: change of notation in sec. 3

References in corpus (4)

• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Magnification relations for Kerr lensing and testing Cosmic Censorship
• A Gauss-Bonnet Type Formula on Riemann-Finsler surfaces with non-constant indicatrix volume

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