Properties of the lens mapping

  • Peter Schneider
  • Jürgen Ehlers
  • Emilio E. Falco
Part of the Astronomy and Astrophysics Library book series (AAL)


In this chapter we describe general properties of the lens mapping. In Sect. 5.1 the basic equations of GL theory are presented and briefly discussed. A general description of the lens mapping in the infinitesimal neighborhood of a point is given in Sect. 5.2. It leads to the concepts of magnification and critical curves and to a classification of ordinary images. In Sect. 5.3 the light-travel-time along ray bundles that correspond to GL images is determined by means of the geometry of wavefronts; this again leads to the connection between Fermat’s principle and the lens mapping. The difference in light-travel-time for different images of a source is an observable; this time delay is one of the central quantities in gravitational lensing. Two general theorems are proved in Sect. 5.4, and a classification of 3-image and 5-image topographies is presented in Sect. 5.5.


Saddle Point Deflection Angle Source Position Lens Plane Observer Position 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Peter Schneider
    • 1
  • Jürgen Ehlers
    • 2
  • Emilio E. Falco
    • 3
  1. 1.Max-Planck-Institut für AstrophysikGarchingGermany
  2. 2.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutPotsdamGermany
  3. 3.Harvard-Smithsonian Center for AstrophysicsCambridgeUSA

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