General Relativity as a SO(3) Gauge-Theory

TL;DR

This paper proposes a new formulation of gravity as an SO(3) gauge theory, introducing a dynamical (1+3) space-time splitting that modifies Einstein's theory, especially at cosmic scales, by adding a new degree of freedom.

Contribution

It introduces a gauge-theoretic approach to general relativity with a dynamical space-time splitting, differing from Einstein's theory by including an additional degree of freedom.

Findings

The theory maintains validity for gravitational phenomena in bounded domains.

It describes the universe's large-scale dynamics through the self-dynamics of space-time splitting.

The empty universe's geometry is characterized by deSitter space, with stable expansion.

Abstract

The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this, in the Newtonian Mechanics space and time obey a absolute, matter-independent meaning. This thesis offers a compromise between the two conceptions: The spontaneous splitting of space-time in a "universal time" and a "absolute space" in the sense of Newton is accepted, but this (1+3)-splitting will receive the status of a dynamical object in the sense of Einstein. Herein, the (large scale) dynamics of the (1+3) splitting is coupled only weakly to the (local) fluctuation of the matter density with the help of the Einsteinian equations, so that these will keep their validity, regarding the gravitational phenomena, in a bounded domain of space (planets, stars, galaxies). However, at a cosmic scale, the properties of the universe as whole will be determined essentially from the selfdynamics of the space-time splitting. The geometry of the (1+3)-splitting and the expansion of the empty universe will be examined in detail. Contrary to the Einsteinian theory, the resulting new theory of gravitation contains a new degree of freedom, that comes into question as a carrier for the energy-momentum tensor of the the gravitational interaction. The "ground state" of the empty universe (-> maximal symmetry)is described by means of a deSitter-geometry, where only the expanding universe renders stable.