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Gravitational lensing by a collection of objects with radial densities

Gravitational lensing by a collection of objects with radial densities In a recent paper by Bayer et al. (Gen Rel Grav 38:1379–1385, 2006), the authors considered a certain class of gravitational lenses consisting of n non-overlapping objects with radial densities. They concluded that there can be at most 6(n − 1) + 1 lensed images of a single light source. The only assumption made on the projected mass density of each object is that it is radial and does not diverge faster than 1/r, where r is the distance to the center of the object. We show that this is too general a class of densities to consider while imposing a bound of 6(n − 1) + 1. We also provide an example to emphasize [together with the results in Bayer et al. (Gen Rel Grav 38:1379–1385, 2006)] that the general problem of finding the correct hypothesis to obtain sharp bounds for the maximal number of images inside the region occupied by masses with radial densities is wide open. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Gravitational lensing by a collection of objects with radial densities

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Mathematical Methods in Physics; Analysis
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-011-0010-5
Publisher site
See Article on Publisher Site

Abstract

In a recent paper by Bayer et al. (Gen Rel Grav 38:1379–1385, 2006), the authors considered a certain class of gravitational lenses consisting of n non-overlapping objects with radial densities. They concluded that there can be at most 6(n − 1) + 1 lensed images of a single light source. The only assumption made on the projected mass density of each object is that it is radial and does not diverge faster than 1/r, where r is the distance to the center of the object. We show that this is too general a class of densities to consider while imposing a bound of 6(n − 1) + 1. We also provide an example to emphasize [together with the results in Bayer et al. (Gen Rel Grav 38:1379–1385, 2006)] that the general problem of finding the correct hypothesis to obtain sharp bounds for the maximal number of images inside the region occupied by masses with radial densities is wide open.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Sep 9, 2011

References