A gravitational lens produces an odd number of images.
Abstract
Rigorous results are given to the effect that a transparent gravitational lens produces an odd number of images. Suppose that p is an event and T the history of a light source in a globally hyperbolic spacetime (M,g). Uhlenbeck's Morse theory of null geodesics is used to show under quite general conditions that if there are at most a finite number n of futuredirected null geodesics from T to p, then M is contractible to a point. Moreover, n is odd and 1/2 (n1) of the images of the source seen by an observer at p have the opposite orientation to the source. An analogous result is noted for Riemannian manifolds with positive definite metric.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 1985
 DOI:
 10.1063/1.526923
 Bibcode:
 1985JMP....26.1592M
 Keywords:

 Gravitational Lenses