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UNDERSTANDING SOLUTIONS OF THE ANGULAR TEUKOLSKY EQUATION IN THE PROLATE ASYMPTOTIC LIMIT

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abstract
Solutions of the angular Teukolsky equation are required to obtain frequency-domain solutions for perturbations on the Kerr geometry. The analytic behavior of solutions to the angular Teukolsky equation have been explored in expansions about the spherical limit, and in the asymptotic oblate limit. However, obtaining the general behavior in the asymptotic prolate limit has proven difficult. We perform a high accuracy study of prolate solutions to the angular Teukolsky equation, and use these to extend our understanding of the analytic behavior of solutions in the asymptotic prolate limit. We found two categories of prolate solutions. One group of solutions, which we call non-anomalous solutions, are in agreement with solutions previously predicted and calculated numerically. The second category of prolate solutions, which we call anomalous solutions, to the best of our knowledge, are a previously unknown set of solutions for the prolate case. The existence of the anomalous solutions strongly affects the transition of the non-anomalous solutions to their asymptotic limit. Based on our understanding of the anomalous solutions, we have extended the polynomial fit of the non-anomalous solutions to higher order than any previous numerical studies. We similarly determined a limited polynomial fit for the anomalous solutions and explored their basic properties. Our hope is that these solutions will provide clarity to, and reduce the computational load on, future studies which require solutions to the angular Teukolsky equation.
subject
Angular Teukolsky Equation
Modes of Kerr
Numerical Methods
Teukolsky Master Equation
contributor
Vickers, Daniel James (author)
Cook, Gregory B. (committee chair)
Carlson, Eric D. (committee member)
Cho, Sam S. (committee member)
date
2021-01-13T09:35:20Z (accessioned)
2021-01-13T09:35:20Z (available)
2020 (issued)
degree
Physics (discipline)
identifier
http://hdl.handle.net/10339/97950 (uri)
language
en (iso)
publisher
Wake Forest University
title
UNDERSTANDING SOLUTIONS OF THE ANGULAR TEUKOLSKY EQUATION IN THE PROLATE ASYMPTOTIC LIMIT
type
Thesis

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