Instanton representation of Plebanski gravity: a conceptual introduction

TL;DR

This paper introduces the instanton representation of Plebanski gravity, explaining its physical implications, equivalence with Plebanski's theory, and properties of gravitational instantons, along with its evolution equations that maintain initial constraints.

Contribution

It provides a comprehensive, self-contained overview of IRPG, highlighting its physical consequences, equivalence with Plebanski's formulation, and the structure of its evolution equations.

Findings

IRPG is equivalent to Plebanski's theory in certain regimes

Gravitational instantons are analyzed within IRPG

IRPG evolution equations preserve initial constraints

Abstract

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.