Gravitational lensing by a collection of objects with radial densities

Abstract

In a recent paper by Bayer et al. (Gen Rel Grav 38:1379–1385, 2006), the authors considered a certain class of gravitational lenses consisting of n non-overlapping objects with radial densities. They concluded that there can be at most 6(n − 1) + 1 lensed images of a single light source. The only assumption made on the projected mass density of each object is that it is radial and does not diverge faster than 1/r, where r is the distance to the center of the object. We show that this is too general a class of densities to consider while imposing a bound of 6(n − 1) + 1. We also provide an example to emphasize [together with the results in Bayer et al. (Gen Rel Grav 38:1379–1385, 2006)] that the general problem of finding the correct hypothesis to obtain sharp bounds for the maximal number of images inside the region occupied by masses with radial densities is wide open.