Date of Award:
Master of Science (MS)
Mathematics and Statistics
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.
Shaw, Benjamin D., "Tractor Connections for Killing Tensors and Their Generalizations" (2021). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 8325.
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