Date of Award
Master of Science (MS)
Mathematics and Statistics
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.
Hicks, Jesse W., "Algebraic Properties of Killing Vectors For Lorentz Metrics In Four Dimensions" (2011). All Graduate Plan B and other Reports. 102.
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