Canonical decomposition of the general relativistic initial value problem

A canonical transformation is employed to implement a conformal transformation of the configuration variables of general relativity. The transformation is so chosen that the spatial constraints become algebraic in the trace of the momentum density. The temporal constraint is then found to have the form of York and O'Murchadha. The role played by the York coordinate condition in decoupling the constraint equations is examined, and a procedure to solve the constraint equations without employing such a coordinate condition is sketched.