Theoretical gravitational lensing. Beyond the weak-field small-angle approximation

Abstract

An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted to analytical methods considering spacetimes in which the equations for light rays (lightlike geodesics) is completely integrable. This includes spherically symmetric static spacetimes, the Kerr spacetime and plane gravitational waves. The second part is devoted to qualitative methods which give some information on lensing properties without actually solving the equation for lightlike geodesics. This includes Morse theory, methods from differential topology and bifurcation theory.

20 pages, 9 figures; extended written version of rapporteur talk, given at the workshop on ``Theoretical Gravitational Lensing'' at the 11th Marcel Grossmann Meeting, Berlin, 2006

Cited by in corpus (6)

• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Metamorphoses of a photon sphere
• Negative Time Delay in Strongly Naked Singularity Lensing
• Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole
• Non-commutativity in Hayward spacetime
• Gravitational signatures of a nonlinear electrodynamics in $f(R,T)$ gravity