Item Details

title

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

author

Vickers, Daniel James

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

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

type

Thesis