Relativity via a Bergmannian Chronometric in a Squared-Dimensional Hyperspace

Details Relativity via a Bergmannian Chronometric in a Squared-Dimensional Hyperspace Relativity via a Bergmannian Chronometric in a Squared-Dimensional Hyperspace

Jan 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........66h&link_type=abstract

Thesis (PH.D.)--GEORGIA INSTITUTE OF TECHNOLOGY, 1990.Source: Dissertation Abstracts International, Volume: 51-09, Section: B, p

Computer Science

Hyperspace

Scientific paper

Einstein's theory of General Relativity describes spacetime under the assumption that it is four dimensional. There are theories of spacetime which assume higher dimensionality and account for the appearance of four dimensions by methods such as lattice compactification. Our research explores an avenue of higher dimensions based on generalized spinors which transform under the special linear group and result in spacetime dimensions which are squares of integers. The Bergmannian chronometrics are not Riemannian, but Finsler in the higher dimensions. Bracket space is introduced in order to show a variety of routes to hyperspace. The field equations differ from Einstein's by replacing a factor of two by the spinorial dimension. Mass is introduced by adding a mass term in the action, which results in a hyper-stress-energy-momentum tensor. The chronometric is not required to be covariantly constant by the hyper -Palatini variations. "Spherical" symmetry in this spacetime is explored, an appropriate set of coordinates is introduced and the invariant for nine dimensional "spherical" symmetry is given. The torsion free plane wave and "spherical" symmetry are examined for nine dimensional spacetime.

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