Plebanski gravity without the simplicity constraints

Abstract

In Plebanski's self-dual formulation general relativity becomes SO(3) BF theory supplemented with the so-called simplicity (or metricity) constraints for the B-field. The main dynamical equation of the theory states that the curvature of the B-compatible SO(3) connection is self-dual, with the notion of self-duality being defined by the B-field. We describe a theory obtained by dropping the metricity constraints, keeping only the requirement that the curvature of the B-compatible connection is self-dual. It turns out that the theory one obtains is to a very large degree fixed by the Bianchi identities. Moreover, it is still a gravity theory, with just two propagating degrees of freedom as in GR.

7 pages

References in corpus (4)

• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• On deformations of Ashtekar's constraint algebra
• Renormalizable Non-Metric Quantum Gravity?

Cited by in corpus (2)

• Modified gravity without new degrees of freedom
• Spherically symmetric black holes in minimally modified self-dual gravity