BF gravity and the Immirzi parameter

TL;DR

This paper introduces a new BF-type formulation of four-dimensional gravity that incorporates an arbitrary Immirzi parameter and constructs an analogue of the Urbantke metric for this model.

Contribution

It generalizes previous BF formulations of gravity to include any Immirzi parameter and develops a corresponding Urbantke metric analogue.

Findings

Successfully incorporates arbitrary Immirzi parameter into BF gravity

Constructs an Urbantke metric analogue for the new model

Provides a generalized framework for BF formulations of gravity

Abstract

We propose a novel BF-type formulation of real four-dimensional gravity, which generalizes previous models. In particular, it allows for an arbitrary Immirzi parameter. We also construct the analogue of the Urbantke metric for this model.