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Existence and blowup results for asymptotically Euclidean initial data sets generated by the conformal method
- Source :
- Physical Review D. 94
- Publication Year :
- 2016
- Publisher :
- American Physical Society (APS), 2016.
-
Abstract
- For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar curvature problem, which provides a necessary condition on the seed data for the conformal constraint equations to (possibly) admit a solution. We then consider sets of asymptotically Euclidean (AE) seed data for which solutions of the conformal constraint equations exist, and examine the blowup properties of these solutions as the seed data sets approach sets for which no solutions exist. We also prove that there are AE seed data sets which include a Yamabe nonpositive metric and lead to solutions of the conformal constraints. These data sets allow the mean curvature function to have zeroes.<br />27 pages
- Subjects :
- Physics
Mean curvature
Extremal length
010308 nuclear & particles physics
Conformal field theory
Prescribed scalar curvature problem
010102 general mathematics
FOS: Physical sciences
Conformal map
General Relativity and Quantum Cosmology (gr-qc)
Function (mathematics)
01 natural sciences
General Relativity and Quantum Cosmology
Constraint (information theory)
Mathematics - Analysis of PDEs
0103 physical sciences
Euclidean geometry
FOS: Mathematics
Applied mathematics
0101 mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 24700029 and 24700010
- Volume :
- 94
- Database :
- OpenAIRE
- Journal :
- Physical Review D
- Accession number :
- edsair.doi.dedup.....d18d801a7d6d681b0575555f84d28fd4
- Full Text :
- https://doi.org/10.1103/physrevd.94.104046