Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

Details Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1 Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

2002-07-22

arxiv.org/abs/gr-qc/0207079v2

Class.Quant.Grav. 19 (2002) 5409-5428

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, no figures; Refs added, typos corrected. To appear in CQG

Scientific paper

10.1088/0264-9381/19/21/307

In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive models. There are in all five different multiply transitive models which cannot be considered as a special case of a simply transitive model. The classification of simply transitive models, relies heavily upon the classification of the four dimensional (real) Lie algebras. For the orthogonal case, we derive all the equations of motion and give some examples of exact solutions. Also the problem of how these models can be compactified in context with the Kaluza-Klein mechanism, is addressed.

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