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Lower Bounds on Image Magnification in Gravitational Lensing

A. O. Petters
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 452, No. 1949 (Jun. 8, 1996), pp. 1475-1490
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52926
Page Count: 16
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Lower Bounds on Image Magnification in Gravitational Lensing
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Abstract

A rigorous study of lower bounds on image magnification in single-plane gravitational lensing is presented. These bounds are determined for the total magnification of point sources undergoing lensing by a general single-plane gravitational lens. The lower bounds are expressed as a function of the number of images of the source, the number of obstruction points of the deflector potential, and mass density of the lens. In particular, our lower bounds adjust according to the multiplicity of the region of the caustic network where the lensed source is located. The results for the general lens are then used to find lower bounds on the total magnification due to non-singular and singular deflectors. The latter lenses are considered in detail for the cases of point-mass deflectors with shear and continuous matter (subcritical, strongly sheared, supercritical, and critical cases). Automatic with this study are general results on image counting and a discussion of the magnifications and trajectories of images of a lensed source as the source moves to `infinity'. The paper uses Morse-theoretic tools, yielding a new approach to the study of lower bounds on image magnification in gravitational lensing.

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