Math @ Duke

Publications [#243970] of Arlie O. Petters
Papers Published
 Petters, AO; Wicklin, FJ, Fixed points due to gravitational lenses,
Journal of Mathematical Physics, vol. 39 no. 2
(January, 1998),
pp. 10111023, AIP Publishing [doi]
(last updated on 2019/07/16)
Abstract: 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 pointmass lenses with continuous matter and shear. Counting formulas and bounds on the number of fixed points are determined. The results include an oddnumber fixedpoint 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.


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