Hilbert Manifold Structure of The Set of Solutions of Constraint   Equations For Coupled Einstein and Scalar Fields
  In this paper, we prove that the set of solutions of constraint equations for coupled Einstein and scalar fields in classical general relativity possesses Hilbert manifold structure. We follow the work of R. Bartnik [2] and use weighted Sobolev spaces and Implicit Function Theorem to prove our results. 
Juhi H. Rai and R.V. Saraykar
gr-qc math.DG