Selfdual 2-form formulation of gravity and classification of energy-momentum tensors

TL;DR

This paper presents a novel Lagrangian formulation of gravity coupled with matter using selfdual 2-forms, classifying energy-momentum tensors and discussing related formulation challenges.

Contribution

It introduces a selfdual 2-form based Lagrangian approach for gravity-matter systems and clarifies issues in pure spin-connection formulations.

Findings

Classifies energy-momentum tensors into irreducibility classes.

Demonstrates a Lagrangian formulation using selfdual 2-forms.

Identifies difficulties and ambiguities in pure spin-connection approaches.

Abstract

It is shown how the different irreducibility classes of the energy-momentum tensor allow for a Lagrangian formulation of the gravity-matter system using a selfdual 2-form as a basic variable. It is pointed out what kind of difficulties arise when attempting to construct a pure spin-connection formulation of the gravity-matter system. Ambiguities in the formulation especially concerning the need for constraints are clarified.