Date of Award:
Doctor of Philosophy (PhD)
Mathematics and Statistics
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.
Hicks, Jesse W., "Classification of Spacetimes with Symmetry" (2016). All Graduate Theses and Dissertations. 5054.