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https://hdl.handle.net/1959.11/18144
Title: | A note on mass-minimising extensions | Contributor(s): | McCormick, Stephen (author) | Publication Date: | 2015 | Open Access: | Yes | DOI: | 10.1007/s10714-015-1993-2 | Handle Link: | https://hdl.handle.net/1959.11/18144 | Open Access Link: | https://arxiv.org/abs/1501.05045 | Abstract: | A conjecture related to the Bartnik quasilocal mass, is that the infimum of the ADM energy, over an appropriate space of extensions to a compact 3-manifold with boundary, is realised by a static metric. It was shown by Corvino (Commun Math Phys 214(1):137-189, 2000) that if the infimum is indeed achieved, then it is achieved by a static metric; however, the more difficult question of whether or not the infimum is achieved, is still an open problem. Bartnik (Commun Anal Geom 13(5):845-885, 2005) then proved that critical points of the ADM mass, over the space of solutions to the Einstein constraints on an asymptotically flat manifold without boundary, correspond to stationary solutions. In that article, he stated that it should be possible to use a similar construction to provide a more natural proof of Corvino's result. In the first part of this note, we discuss the required modifications to Bartnik's argument to adapt it to include a boundary. Assuming that certain results concerning a Hilbert manifold structure for the space of solutions carry over to the case considered here, we then demonstrate how Bartnik's proof can be modified to consider the simpler case of scalar-flat extensions and obtain Corvino's result. In the second part of this note, we consider a space of extensions in a fixed conformal class. Sufficient conditions are given to ensure that the infimum is realised within this class. | Publication Type: | Journal Article | Source of Publication: | General Relativity and Gravitation, 47(12), p. 1-14 | Publisher: | Springer New York LLC | Place of Publication: | United States of America | ISSN: | 1572-9532 0001-7701 |
Fields of Research (FoR) 2008: | 010504 Mathematical Aspects of General Relativity 010110 Partial Differential Equations |
Fields of Research (FoR) 2020: | 490204 Mathematical aspects of general relativity 490410 Partial differential equations |
Socio-Economic Objective (SEO) 2008: | 970102 Expanding Knowledge in the Physical Sciences 970101 Expanding Knowledge in the Mathematical Sciences |
Socio-Economic Objective (SEO) 2020: | 280120 Expanding knowledge in the physical sciences 280118 Expanding knowledge in the mathematical sciences |
Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article School of Science and Technology |
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