| Summary: | Gravitational lensing, initially a phenomenon used as a solid confirmation of General Relativity, has defined itself in the past decade as a standard astrophysical tool. The ability of a lensing system to produce multiple images of a luminous source is one of the aspects of gravitational lensing that is exploited both theoretically and observationally to improve our understanding of the Universe.
In this thesis, within the field of multiple imaging we explore the case of maximal lensing, that is, the configurations and conditions under which a set of deflecting masses can produce the maximum number of images of a distant luminous source, as well as a study of the value for this maximum number itself.
We study the case of a symmetric distribution of n-1 point-mass lenses at the vertices of a regular polygon of n-1 sides. By the addition of a perturbation in the form of an n-th mass at the center of the polygon it is proven that, as long as the mass is small enough, the system is a maximal lensing configuration that produces 5(n-1) images. Using the explicit value for the upper bound on the central mass that leads to maximal lensing, we illustrate how this result can be used to find and constrain the mass of planets or brown dwarfs in multiple star systems.
For the case of more realistic mass distributions, we prove that when a point-mass is replaced with a distributed lens that does not overlap with existing images or lensing objects, an additional image is formed within the distributed mass while positions and numbers of existing images are left unchanged. This is then used to conclude that the maximum number of images that n isolated distributed lenses can produce is 6(n-1)+1.
In order to explore the likelihood of observational verification, we analyze the stability properties of the symmetric maximal lensing configurations. Finally, for the cases of n=4, 5, and 6 point-mass lenses, we study asymmetric maximal lensing configurations and compare their stability properties against the symmetric case.
|
|---|
