Canonical analysis of unimodular Plebański gravity

Abstract

We present the canonical analysis of different versions of unimodular gravity defined in the Plebański formalism, based on a (generally complex) SO(3) spin connection and set of (self-dual) two-forms. As in the metric formulation of unimodular gravity, one can study either a theory with fixed volume form or work in a parametrised formalism in which the cosmological constant becomes a dynamical field, constrained to be constant by the field equations. In the first case, the Hamiltonian density contains a part which is not constrained to vanish, but rather constrained to be constant, again as in the metric formulation. We also discuss reality conditions and challenges in extracting Lorentzian solutions.

arXiv comment10 pages, two-column revtex; v2: fixed typos, to appear in Phys. Rev. D; v3: more typos fixed

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