Hilbert Manifold Structure of The Set of Solutions of Constraint Equations For Coupled Einstein and Scalar Fields. arXiv:1605.08858
Preprint, arXiv:1605.08858 [gr-qc] (2016).
Summary: 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.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 58D17 | Manifolds of metrics (especially Riemannian) |
| 58J05 | Elliptic equations on manifolds, general theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 58D17 | Manifolds of metrics (especially Riemannian) |
| 58J05 | Elliptic equations on manifolds, general theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
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