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

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

2007-04-26

arxiv.org/abs/0704.3595v5

Nucl. Phys. B, Vol. 852 (2011) pp.681-695

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages. Background material for revised journal article

Scientific paper

10.1016/j.nuclphysb.2011.07.004

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 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 Einsteins spaces, to include more general spacetime geometries.

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