Instanton representation of Plebanski gravity: XIII. Canonical structure   of the Petrov classification of nondegenerate spacetimes
  The instanton representation of Plebanski gravity admits a natural canonical structure where the (densitized) eigenvalues of the CDJ matrix are the basic momentum space variables. Canonically conjugate configuration variables exist for six distinct configurations in the full theory, referred to as quantizable configurations. The CDJ matrix relates to the Petrov classification and principal null directions of spacetime, which we directly correlate to these quantizable degrees of freedom. The implication of this result is the ability to perform a quantization procedure for spacetimes of Petrov Type I, D, and O, using the instanton representation. 
Eyo Ita