Classification of multidimensional spacetimes |
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| Affiliation: | 1. Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, Göttingen 37077, Germany;2. Universite Libre de Bruxelles (ULB), Interdisciplinary Center for Nonlinear Phenomena and Complex Systems, Campus Plaine, CP 231, Blvd. du Triomphe, Brussels B-1050, Belgium;3. Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA;4. National Research University Higher School of Economics, Moscow 101000, Russia;1. Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA;2. National Research University Higher School of Economics, Moscow 101000, Russia |
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| Abstract: | We classify all eleven-dimensional spatially homogeneous spacetimes, which contain a seven-dimensional compact subspace and admit a simple-transitive group of isometry, by enumerating the real ten-dimensional Lie algebras which contain an n-dimensional (n⩾7) compact Lie subalgebra. The main result of this paper consists in giving a complete list of the distinct real ten-dimensional algebras which admit a non-trivial Levi decomposition. It is hoped that this investigation may be of some help in studying eleven-dimensional and ten-dimensional cosmologies which are considered in the context of Kaluza-Klein, supergravity and superstring theories. |
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