Plebanski gravity without the simplicity constraints

Details Plebanski gravity without the simplicity constraints Plebanski gravity without the simplicity constraints

2008-11-19

arxiv.org/abs/0811.3147v1

Class.Quant.Grav.26:055002,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages

Scientific paper

10.1088/0264-9381/26/5/055002

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.

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