Stationary or static space-times and Young tableaux
<|reference_start|>Stationary or static space-times and Young tableaux: Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors \theta with 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 \theta. The tensor \theta is connected with the timelike Killing vector field of the space-time. \theta lies 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.<|reference_end|>
@article{fiedler2005stationary,
    title={Stationary or static space-times and Young tableaux},
    author={Bernd Fiedler},
    journal={J.Phys.Conf.Ser.30:152-162,2006},
    year={2005},
    doi={10.1088/1742-6596/30/1/018},
    archivePrefix={arXiv},
    eprint={math/0510304},
    primaryClass={math.DG cs.SC gr-qc math.CO}
}