Minimally modified self-dual 2-forms gravity

TL;DR

This paper explores a minimal perturbative modification of the self-dual 2-forms formulation of complex general relativity, analyzing the geometric interpretation of the altered field variables compared to the original Plebanski formulation.

Contribution

It provides a detailed investigation of the geometric meaning of Krasnov's minimal modification of the self-dual 2-forms gravity, contrasting it with the original Plebanski variables.

Findings

Clarifies the geometric interpretation of modified field variables

Shows how minimal modifications affect the original formulation

Provides insights into the structure of generalized gravity theories

Abstract

The first order Plebanski formulation of (complex) general relativity (GR) in terms of self-dual 2-forms admits a generalization, proposed by Krasnov, that is qualitatively different from other possible generalizations of GR in terms of metric variables. In this paper, we investigate, within a minimal modification, and in a perturbative approach, the geometrical meaning of the field variables used in the Krasnov generalization, and compare them to the field variables used in the Plebanski formulation.