Pictures of gravitational lensing

Abstract

Graphic descriptions of gravitational lensing are presented as a means to elaborate on a historical overview of the field. The time delay with respect to a reference plane, momentum, and gravitational deflection is considered in terms of the geometrical construction of images in lensing based on wavefronts. The seminal works of Fermat, Huyghens, Malus and Hamilton are listed; Refsdal's work (1964) is covered; and special attention is given to Arnold's work on catastrophe theory (1984), Schneider's amplification theorem (1984), and studies by Berry and Upstill (1980). The different approaches to lensing are illustrated for a simple two-dimensional case based on either rays, wavefronts, or phase space, which are then discussed mathematically. The principal directions of curvature are shown for a wavefront passing through a lens, and the behavior of critical lines near an umbilic point is discussed.