Utah State University

Title

Algebraic Properties of Killing Vectors For Lorentz Metrics In Four Dimensions

Author

Jesse W. Hicks, Utah State University

Date of Award

12-2011

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Ian Anderson

Abstract

Four-dimensional space-times with symmetry play a central role in the theory of general relativity. In 1961, in the book Einstein Spaces, A.Z. Petrov gave a complete local classification of four-dimensional space-times based upon their local isometry group, that is, their Lie algebra of Killing vector fields. In this report we discuss algebraic and geometric properties of these Lie algebras. A database of these properties has been computed for the five-dimensional Lie algebras of Killing vectors found in Petrov. As an application of our work, we present dieomorphisms between a few pairs of these Lie algebras of Killing vectors.

Comments

This work made publicly available electronically on April 12, 2012.

Recommended Citation

Hicks, Jesse W., "Algebraic Properties of Killing Vectors For Lorentz Metrics In Four Dimensions" (2011). All Graduate Plan B and other Reports. Paper 102.
http://digitalcommons.usu.edu/gradreports/102

4-12-2012