Instanton Representation of Plebanski Gravity. The Classical Theory

This paper is a self-contained introduction to the instanton representation of Plebanski gravity (IRPG), a formulation of General Relativity (GR) where the basic variables are a spacetime gauge connection and a three by three matrix valued in the Lie algebra of so(3,C). We present a classical analysis of the IRPG from various perspectives, noting some of its interesting features and motivations.