4-dimensional General Relativity from the instrinsic spatial geometry of SO(3)SO(3) Yang–Mills theory

In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang–Mills theory which has been exposed by previous authors as well as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang–Mills theory where the antiself-dual Weyl curvature replaces the Yang–Mills coupling constant. We have generalized the results of some previous authors, covering Einsteinʼs spaces, to include more general spacetime geometries.