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

M. J. Reboucas·J. Santos·A. F. F. Teixeira
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Abstract

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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M. J. Reboucas, J. Santos, A. F. F. Teixeira. 2003-12-12. Classification of Energy Momentum Tensors in $n \geq 5$ Dimensional Space-times: a Review. https://doi.org/10.1590/s0103-97332004000300034

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