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.

arXiv comment18 pages

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Cited by in corpus (8)

• Identification of black hole horizons using scalar curvature invariants
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Jet Bundle Geometry of Scalar Field Theories
• Curvature invariant characterization of event horizons of four-dimensional black holes conformal to stationary black holes
• Cartan Invariants and Event Horizon Detection, Extended Version
• An Invariant Characterization of the Levi-Civita Spacetimes
• $\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds
• On the Equivalence of Spacetimes, the Cartan-Karlhede Algorithm