Gravitational lensing by Elliptical Galaxies, and the Schwarz Function

Details Gravitational lensing by Elliptical Galaxies, and the Schwarz Function Gravitational lensing by Elliptical Galaxies, and the Schwarz Function

2007-08-20

arxiv.org/abs/0708.2684v1

Physics

Mathematical Physics

16 pages, 7 figures based on a pleanry talk at the international conference on analysis and mathematical physics "New Trends i

Scientific paper

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.

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