Instanton representation of Plebanski gravity: a conceptual introduction

This paper presents a self-contained introduction into the instanton representation of Plebanski gravity (IRPG), a GR formulation which uses a gauge connection and a three by three matrix as basic variables. In this paper we explore some physical consequences of the IRPG both from the 3+1 and from the covariant perspectives, including its regime of equivalence with Plebanski's theory, and gravitational instantons. We conclude with the IRPG evolution equations, which are shown to preserve the initial value constraints of the theory.