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Formation of arcs by nearly circular gravitational lenses.

An extended source located near the axis of a nearly circular, sufficiently nonlinear lens can produce extended-arc-like images. Examples of these may have been found near three distant clusters of galaxies which seem to be acting as gravitational lenses. We propose a simple geometrical method for locating images of objects using the Einstein ring and the corresponding caustic. We also give an approximate theory of lenses for which deviations from circularity are small perturbations. We discuss noncircular perturbations of practical interest for gravitational lensing and properties of the arcs that are thus formed.