Title: The Cartan Algorithm in Five Dimensions,
Abstract: In this paper we introduce an algorithm to determine the equivalence of five
dimensional spacetimes, which generalizes the Karlhede algorithm for four
dimensional general relativity. As an alternative to the Petrov type
classification, we employ the alignment classification to algebraically
classify the Weyl tensor. To illustrate the algorithm we discuss three
examples: the singly rotating Myers-Perry solution, the Kerr (anti) de Sitter
solution, and the rotating black ring solution. We briefly discuss some
applications of the Cartan algorithm in five dimensions.