Classification of Energy Momentum Tensors in $n \geq 5$ Dimensional Space-times: a Review

Details Classification of Energy Momentum Tensors in $n \geq 5$ Dimensional Space-times: a Review Classification of Energy Momentum Tensors in $n \geq 5$ Dimensional Space-times: a Review

2003-12-12

arxiv.org/abs/gr-qc/0312064v1

Braz.J.Phys. 34 (2004) 535-543

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTex2e, 18 pages. To appear in Braz.J.Phys (2004)

Scientific paper

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of a great number of 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 review the main results on the algebraic classification of second order symmetric tensors in 5-dimensional space-times. All possible Segre types for a symmetric two-tensor are found, and a set of canonical forms for each Segre type is obtained. A limiting diagram for the Segre types of these symmetric tensors in 5-D is built. Two theorems which collect together some basic results on the algebraic structure of second order symmetric tensors in 5-D are presented. We also show how one can obtain, by induction, the classification and the canonical forms of a symmetric two-tensor on n-dimensional (n > 5) spaces from its classification in 5-D spaces, present the Segre types in n-D and the corresponding canonical forms. This classification of symmetric two-tensors in any n-D spaces and their canonical forms are important in the context of n-dimensional brane-worlds context and also in the framework of 11-D supergravity and 10-D superstrings.

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