The Jacobi map for gravitational lensing: the role of the exponential map

Abstract

We present a formal derivation of the key equations governing gravitational lensing in arbitrary space-times, starting from the basic properties of Jacobi fields and their expressions in terms of the exponential map. A careful analysis of Jacobi fields and Jacobi classes near the origin of a light beam determines the nature of the singular behavior of the optical deformation matrix. We also show that potential problems that could arise from this singularity do not invalidate the conclusions of the original argument presented by Seitz, Schneider & Ehlers (1994).

"Minor revisions; matches version published in Class. Q. Grav. 30 (2013) 065020

References in corpus (2)

• On the generalized Jacobi equation
• The Jacobi map for gravitational lensing: the role of the exponential map

Cited by in corpus (4)

• Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models
• The Jacobi map for gravitational lensing: the role of the exponential map
• 1+1+2 covariant formulation of light propagation in spacetime
• Exponential-wrapped distributions on symmetric spaces