Instanton representation of Plebanski gravity. Consistency of the initital value constraints under time evolution

The instanton representation of Plebanski gravity provides as equations of motion a Hodge self-duality condition and a set of `generalized’ Maxwell’s equations, subject to gravitational degrees of freedom encoded in the initial value constraints of general relativity. The main result of the present paper will be to prove that this constraint surface is preserved under time evolution. We carry this out not using the usual Dirac procedure, but rather the Lagrangian equations of motion themsleves. Finally, we provide a comparison with the Ashtekar formulation to place these results into overall context.