General Relativity and the Theory of a Self-Interacting Abelian Gauge Field

Abstract

The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor. In this paper, the equations of the standard theory of GR using the parametric representation are first developed. Afterwards, the fundamental ideas of a new type of abelian self-interacting gauge theory are presented. Finally, it is shown that the gauge field equations of this new theory are identical to the parametric form of Einstein’s equations of general relativity. It is concluded that classical gravity can be described either by the usual theory of GR in a curved space-time or, alternatively as a self-interacting gauge theory independent of the dynamics of space-time.