The group‐theoretical classification of the 11‐dimensional classical homogeneous Kaluza–Klein cosmologies

• Published in: Journal of mathematical physics 1987-01, Vol.28 (1), p.171-173
• Main Authors: Demiański, M., Golda, Z., Sokol/owski, L. M., Szydl/owski, M., Turkowski, P.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; General relativity and gravitation; Gravity in more than four dimensions, kaluza-klein theory, unified field theories; alternative theories of gravity; Physics
• ISSN: 0022-2488; 1089-7658
• DOI: 10.1063/1.527784

In the context of the classical Kaluza–Klein cosmology the generalized Bianchi models in 11 dimensions are considered. These are space‐times whose spacelike ten‐dimensional sections are the hypersurfaces of transitivity for a ten‐dimensional isometry group of the total space‐time. Such a space‐time is a trivial principal fiber bundle P(M,G 7), where M is a four‐dimensional physical space‐time with an isometry group G 3 (of a Bianchi type) and G 7 is a compact isometry group of the compact internal space. The isometry group of P is G 1 0=G 3⊗G 7, hence all the generalized Bianchi models are classified by enumerating the relevant groups G 7. Due to the compactness of G 7 the result is astonishingly simple: there are three distinct homogeneous internal spaces in addition to the 11 ordinary Bianchi types for M.