Abelian decomposition of Einstein’s theory: Restricted gravity

Abstract

Treating Einstein’s theory as the gauge theory of Lorentz group, we discuss the Abelian decomposition of Einstein’s theory and show that in restricted gravity the graviton is described by the spin-one gauge potential. This establishes the Abelian dominance in Einstein’s theory, that the core dynamics of Einstein’s theory is described by restricted gravity obtained by the Abelian projection of Einstein’s theory. We discuss physical implications of our results.