THE POST-BIANCHI IDENTITIES IN THE GHP FORMALISM

As is well-known, when searching for Petrov type I vacuum solutions the imposition of tetrad conditions leads to integrability conditions on the Bianchi identities. Such post-Bianchi equations are simplest in GHP. They are exhibited explicitly for both a “canonical” frame and an “aligned” frame. Choosing a particular gauge, however, complicates the situation considerably; many more conditions are obtained. When this is done for the “canonical” case the resulting equations, when translated to NP, are the Brans-Edgar equations. How all such equations can be checked is reviewed in some detail.