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https://hdl.handle.net/1959.11/16083
Title: | The phase space for the Einstein-Yang-Mills equations and the first law of black hole thermodynamics | Contributor(s): | McCormick, Stephen (author) | Publication Date: | 2014 | Open Access: | Yes | DOI: | 10.4310/ATMP.2014.v18.n4.a2 | Handle Link: | https://hdl.handle.net/1959.11/16083 | Open Access Link: | https://arxiv.org/abs/1302.1237 | Abstract: | We use the techniques of Bartnik [5] to show that the space of solutions to the Einstein-Yang-Mills constraint equations on an asymptotically flat manifold with one end and zero boundary components, has a Hilbert manifold structure; the Einstein-Maxwell system can be considered as a special case. This is equivalent to the property of linearisation stability, which was studied in depth throughout the 70s [1, 2, 9, 11, 13, 18, 19]. This framework allows us to prove a conjecture of Sudarsky and Wald [22], namely that the validity of the first law of black hole thermodynamics is a suitable condition for stationarity. Since we work with a single end and no boundary conditions, this is equivalent to critical points of the ADM mass subject to variations fixing the Yang Mills charge corresponding exactly to stationary solutions. The natural extension to this work is to prove the second conjecture from [22], which is the case where an interior boundary is present; this will be addressed in future work. | Publication Type: | Journal Article | Source of Publication: | Advances in Theoretical and Mathematical Physics, 18(4), p. 799-825 | Publisher: | International Press | Place of Publication: | United States of America | ISSN: | 1095-0753 1095-0761 |
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: | 970101 Expanding Knowledge in the Mathematical Sciences 970102 Expanding Knowledge in the Physical Sciences |
Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences 280120 Expanding knowledge in the physical 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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