Abstract
We explore an avenue of higher-dimensional spacetimes based on generalized spinors which transform under the special linear groups and result in spacetime dimensions which are squares of integers. The Bergmannian chronometrics are not Riemannian, but Finslerian in the higher dimensions. The general concept of bracket space is introduced in order to show a variety of routes to hyperspace. The field equations found generalize Einstein's by replacing a factor of two by the spinorial dimension. A mass term is introduced in the action, which results in a hyper-stress-energy-momentum tensor. The chronometric is not required to be covariantly constant under the hyper-Palatini variations: there is torsion. “Spherical” symmetry in this spacetime is explored, an appropriate set of coordinates is introduced, and the invariant for nine-dimensional “spherical” symmetry is given.
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Honeycutt, D.C. Bergmannian relativity and bracket spaces. Int J Theor Phys 30, 1613–1644 (1991). https://doi.org/10.1007/BF00673639
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DOI: https://doi.org/10.1007/BF00673639