Fixed points due to gravitational lenses.

Mathematics – Mathematical Physics

Scientific paper

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Gravitational Lenses

Scientific paper

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. The authors 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.

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