Date of Award
2022
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Lundberg, Erik
Abstract
Due to the phenomenon of gravitational lensing, light from distant sources may appear as several images. The “image counting problem from gravitational lensing" refers to the question of how many images might occur, given a particular distribution of lensing masses. A common model treats the lensing masses as a finite collection of points situated in a finite collection of planes. The position of the apparent images correspond to the critical points of a real-valued function and also as solutions to a system of complex rational equations. Herein, we give upper bounds for the number of images in a point mass multiplane ensemble with an arbitrary number of masses in an arbitrary number of planes. We give lower bounds on the number of solutions in a closely related problem concerning gravitational equilibria. We use persistence homology to investigate two different stochastic ensembles. Finally we produce a multiplane ensemble, related to the maximal one plane ensemble, that produces a large number of images.
Extent
105 p.
Recommended Citation
Perry, Sean, "ON THE IMAGE COUNTING PROBLEM FROM GRAVITATIONAL LENSING" (2022). Electronic Theses and Dissertations 2020 - Present. 1000.
https://digitalcommons.fau.edu/etd_general/1000
Identifier
FA00013889
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2022.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.