The Karlhede classification and derivative bounds

Abstract

This thesis describes the Karlhede classification of a spacetime, this classification providing a means of tackling the well known equivalence problem in general relativity. The Karlhede classification is performed on a number of cylindrically symmetric and stationary axisymmetric spacetimes, and the results given. An invariant classification scheme is presented for vacuum type D and vacuum type N spacetimes, and a canonical form is derived for each of the resulting classes, these canonical forms forming an essential part of the Karlhede classification. In addition the theoretical upper bound on the order of covariant derivative of the Riemann tensor required to peform a Karlhede classification is examined and reduced for a number of cases.

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