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.
Highlights
In its most general sense, gravitational lensing is a collective term for all effects of a gravitational field on the propagation of electromagnetic radiation, with the latter usually described in terms of rays
The gravitational field is coded in a metric of Lorentzian signature on the 4-dimensional spacetime manifold, and the light rays are the lightlike geodesics of this spacetime metric
We first summarize results on the lightlike geodesics that hold in arbitrary spacetimes
Summary
In its most general sense, gravitational lensing is a collective term for all effects of a gravitational field on the propagation of electromagnetic radiation, with the latter usually described in terms of rays. The quasi-Newtonian approximation formalism has proven very successful for using gravitational lensing as a tool in astrophysics This is impressively demonstrated by the work reviewed in [343]. General theorems on lensing (e.g., criteria for multiple imaging, characterizations of caustics, etc.) should be formulated within the exact spacetime setting of general relativity, if possible, to make sure that they are not just an artifact of approximative assumptions. The ray-optical treatment used throughout this review is the standard high-frequency approximation (geometric optics approximation) of the electromagnetic theory for light propagation in vacuum on a general-relativistic spacetime (see, e.g., [225], § 22.5 or [299], Section 3.2). Minkowski spacetime is taken as the background, and again the lenses need not be thin and may be moving
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