A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology

Details A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology

2003-11-20

arxiv.org/abs/gr-qc/0311068v1

Mod.Phys.Lett. A18 (2003) 2807-2816

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, to appear in Mod. Phys. Lett. A (2003) in the present form

Scientific paper

10.1142/S0217732303012179

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we reexamine the classification of the second order symmetric tensors in 5--D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in 5-dimensional space-times. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional spaces from the classification on 4-dimensional spaces. This is important in the context of 11--D supergravity and 10--D superstrings.

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