Transcendental Harmonic Mappings and Gravitational Lensing by Isothermal Galaxies

Details Transcendental Harmonic Mappings and Gravitational Lensing by Isothermal Galaxies Transcendental Harmonic Mappings and Gravitational Lensing by Isothermal Galaxies

2009-08-23

arxiv.org/abs/0908.3310v1

Physics

Mathematical Physics

11 pages, 3 figures

Scientific paper

Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four ``bright'' images of a single source. The more physically interesting example of an isothermal galaxy has density that is constant on \emph{homothetic} ellipses. In that case bright images can be seen to correspond to zeros of a certain transcendental harmonic mapping. We use complex dynamics to give an upper bound on the total number of such zeros.

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