# Gravitational Lensing from a Spacetime Perspective

**Volker Perlick
**

Institute of Theoretical Physics

TU Berlin

Sekr. PN 7-1

Hardenbergstrasse 36

10623 Berlin

Germany

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Abstract

The theory of gravitational lensing is reviewed from a spacetime perspective, without
quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational
lensing where light propagation is described in terms of lightlike geodesics of a metric of
Lorentzian signature. It includes the basic equations and the relevant techniques for calculating
the position, the shape, and the brightness of images in an arbitrary general-relativistic
spacetime. It also includes general theorems on the classification of caustics, on criteria for
multiple imaging, and on the possible number of images. The general results are illustrated
with examples of spacetimes where the lensing features can be explicitly calculated, including
the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane
gravitational waves, and others.