Statistics of extreme gravitational lensing events. I. The zero shear case

For a given source and lens pair, there is a thin on-axis tubelike volume behind the lens in which the radiation flux from the source is greatly increased due to gravitational lensing. Any objects (such as dust grains) that pass through such a thin tube will experience strong bursts of radiation, i.e., extreme gravitational lensing events (EGLEs). We study the physics and statistics of EGLEs for the case in which finite source size is more important than shear. One of the several possible significant astrophysical effects is investigated with an illustrative calculation.