2-Form Gravity of the Lorentzian Signature

TL;DR

This paper presents a novel 2-form, BF-like action for Lorentzian Einstein gravity using only the self-dual connection, offering a new perspective on classical canonical formulations.

Contribution

It introduces the first known 2-form action for Lorentzian gravity that employs only the self-dual connection, expanding the theoretical framework.

Findings

The action describes real Lorentzian gravity.

Classical canonical theory aligns with Einstein-Ashtekar formulation plus reality conditions.

Provides a new spinorial, BF-like approach to gravity.

Abstract

We introduce a new spinorial, BF-like action for the Einstein gravity. This is a first, up to our knowledge, 2-form action which describes the real, Lorentzian gravity and uses only the self-dual connection. In the generic case, the corresponding classical canonical theory is equivalent to the Einstein-Ashtekar theory plus the reality conditions.