Date of Award:

2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

Ian Anderson

Abstract

Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we

i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes;

ii) create digital databases of the classification for easy access and use for researchers;

iii) create software to classify any spacetime metric with symmetry against the new database;

iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics;

v) classify spacetimes with symmetry in the book Exact Solutions to Einstein’s Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov’s paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.

Checksum

977c7f28e3b6b70879ed86038b81942b

Included in

Mathematics Commons

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