Date of Award:

12-2021

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Ian Anderson

Committee

Ian Anderson

Committee

Mark Fels

Committee

Charles Torre

Abstract

We create new symbolic software tools for the analysis of Killing tensors. Central to our work is the construction of the tractor connection defined on the tractor bundle, which allows one to obtain information about the space of Killing tensors without solving the Killing equations–an approach termed the tractor approach. We give a new application of the tractor approach which allows one to more easily check explicitly for linear independence of a given set of Killing tensors. We develop software to implement such methods in the case of rank 2 Killing tensors; similarly, we develop software to implement analogous methods in the study of Killing-Yano tensors and conformal Killing vectors. Using our newly developed software, we find examples of rank 2 irreducible Killing tensors for exact solutions to Einstein’s field equations. We also make an in-depth study of various other methods of constructing Killing tensors of rank 2 and find that these algorithms most often do not produce Killing tensors which are linearly independent of the reducible Killing tensors and the metric, with the Kerr metric being one of the only known sources of examples.

Checksum

635a929204350fc25698c2eb24bdd3c5

Download

Included in

Mathematics Commons

Share

COinS

Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .