Living Reviews in Relativity

"Gravitational Lensing from a Spacetime Perspective"
Volker Perlick  

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1 Introduction
2 Lensing in Arbitrary Spacetimes
2.1 Light cone and exact lens map
2.2 Wave fronts
2.3 Optical scalars and Sachs equations
2.4 Distance measures
2.5 Image distortion
2.6 Brightness of images
2.7 Conjugate points and cut points
2.8 Criteria for multiple imaging
2.9 Fermat’s principle for light rays
3 Lensing in Globally Hyperbolic Spacetimes
3.1 Criteria for multiple imaging in globally hyperbolic spacetimes
3.2 Wave fronts in globally hyperbolic spacetimes
3.3 Fermat’s principle and Morse theory in globally hyperbolic spacetimes
3.4 Lensing in asymptotically simple and empty spacetimes
4 Lensing in Spacetimes with Symmetry
4.1 Lensing in conformally flat spacetimes
4.2 Lensing in conformally stationary spacetimes
4.3 Lensing in spherically symmetric and static spacetimes
4.4 Lensing in axisymmetric stationary spacetimes
5 Examples
5.1 Schwarzschild spacetime
5.2 Kottler spacetime
5.3 Reissner–Nordström spacetime
5.4 Morris–Thorne wormholes
5.5 Barriola–Vilenkin monopole
5.6 Janis–Newman–Winicour spacetime
5.7 Boson and fermion stars
5.8 Kerr spacetime
5.9 Rotating disk of dust
5.10 Straight spinning string
5.11 Plane gravitational waves
6 Acknowledgements
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