Gravitational lensing by Elliptical Galaxies, and the Schwarz Function

Understand

We discuss gravitational lensing by elliptical galaxies with some particular mass distributions.

• Using simple techniques from the theory of quadrature domains and the Schwarz function (cf.
• \cite{Sh}) we show that when the mass density is constant on confocal ellipses, the total number of lensed images of a point source cannot exceed 5 (4 bright images and 1 dim image).
• Also, using the Dive--Nikliborc converse of the celebrated Newton's theorem concerning the potentials of ellipsoids, we show that ``Einstein rings'' must always be either circles (in the absence of a tidal shear), or ellipses.