Fixed points due to gravitational lenses


Journal Article

A fixed point of a gravitational lensing map represents those positions from which a pointlike light source has a lensed image that, despite gravitational lensing, corresponds to the original position of the source. In this paper we study fixed points of lensing maps due to a generic gravitational lens with applications to nonsingular isolated lenses, and to point-mass lenses with continuous matter and shear. Counting formulas and bounds on the number of fixed points are determined. The results include an odd-number fixed-point theorem for nonsingular isolated deflectors. Information on the positions of fixed points are found for the case of point masses on a lens plane with and without shear. The methods of the paper are based on Morse theory, complex variables, and resultants. © 1998 American Institute of Physics.

Full Text

Duke Authors

Cited Authors

  • Petters, AO; Wicklin, FJ

Published Date

  • January 1, 1998

Published In

Volume / Issue

  • 39 / 2

Start / End Page

  • 1011 - 1023

International Standard Serial Number (ISSN)

  • 0022-2488

Digital Object Identifier (DOI)

  • 10.1063/1.532367

Citation Source

  • Scopus