Gravitational Lensing by Elliptical Galaxies, and the Schwarz Function

  • C.D. Fassnacht
  • C.R. Keeton
  • D. Khavinson
Part of the Trends in Mathematics book series (TM)


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. [18]) 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.


Elliptical Galaxy Bright Image Quadrature Domain Gravitational Lens Point Light Source 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • C.D. Fassnacht
    • 1
  • C.R. Keeton
    • 2
  • D. Khavinson
    • 3
  1. 1.Department of PhysicsUniversity of California at DavisDavisUSA
  2. 2.Department of Physics and AstronomyRutgers UniversityPiscatawayUSA
  3. 3.Department of Mathematics & StatisticsUniversity of South FloridaTampaUSA

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