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Existence and blowup results for asymptotically Euclidean initial data sets generated by the conformal method

Authors :
James Dilts
James Isenberg
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

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