Hilbert Manifold Structure of The Set of Solutions of Constraint Equations For Coupled Einstein and Scalar Fields

Abstract

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.

20 pages, submitted for publication. arXiv admin note: text overlap with arXiv:gr-qc/0402070 by other authors