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arXiv · math/0510304

Stationary or static space-times and Young tableaux

Bernd Fiedler
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Abstract

Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors θwith an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators on the basis of S or A realized by differentiable tensor fields in a natural way. We show that certain curvature formulas for stationary or static space-times contain such differentiable realizations of generators based on θ. The tensor θis connected with the timelike Killing vector field of the space-time. θlies in a special symmetry class from the infinite family of irreducible (2,1)-symmetry classes. We determine characteristics of this class. In particular, this class allows a maximal reduction of the length of the curvature formulas. We use a projection formalism by Vladimirov, Young symmetrizers and Littlewood-Richardson products. Computer calculations were carried out by means of the packages Ricci and PERMS.

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Bernd Fiedler. 2005-10-14. Stationary or static space-times and Young tableaux. https://doi.org/10.1088/1742-6596%2F30%2F1%2F018

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