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

2016/05/28 by Juhi H. Rai, Rai, Juhi H., R. V. Saraykar +1 · 1 citation
Mathematics · Physics and Astronomy · #46E35 #58D17 #58J05 #83C05 #83C05. 58D17 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #gr-qc #math.DG #msc:46E35 #msc:58D17 #msc:58J05 #msc:83C05 #msc:83C05.

paper · pdf · doi:10.48550/arxiv.1605.08858

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

arxiv created 2016/05/28 · openalex publication_date 2016/05/28 · arxiv updated 2016/05/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• The mass of an asymptotically flat manifold
• Phase space for the Einstein equations

Cited by

• Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

Related

• Bartnik Hilbert manifold structure on fibers of the scalar curvature and the constraint operator
• The Constraint Equations
• Phase space for the Einstein equations
• The Einstein-scalar field constraints on asymptotically Euclidean manifolds
• Einstein Constraint Equations for Kaluza-Klein Spacetimes