English

The Cartan Algorithm in Five Dimensions

General Relativity and Quantum Cosmology 2017-04-12 v1 Differential Geometry

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.

Keywords

Cite

@article{arxiv.1704.03061,
  title  = {The Cartan Algorithm in Five Dimensions},
  author = {D. D. McNutt and A. A. Coley and A. Forget},
  journal= {arXiv preprint arXiv:1704.03061},
  year   = {2017}
}

Comments

18 pages

R2 v1 2026-06-22T19:13:26.395Z