Classification of Spacetimes with Symmetry

Author

Jesse W. Hicks, Utah State UniversityFollow

Date of Award:

5-2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Ian Anderson

Committee

Ian Anderson

Committee

Zhaohu Nie

Committee

Mark Fels

Committee

Charles Torre

Committee

Andreas Malmendier

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

ff6dd15be38944c9be82b77de85e639e

Recommended Citation

Hicks, Jesse W., "Classification of Spacetimes with Symmetry" (2016). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 5054.
https://digitalcommons.usu.edu/etd/5054