Choquet-Bruhat, Yvonne and Marsden, Jerrold E. (1976) Solution of the Local Mass Problem in General Relativity. Communications in Mathematical Physics, 51 (3). pp. 283-296. ISSN 0010-3616 http://resolver.caltech.edu/CaltechAUTHORS:20100730-082059316
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The local mass problem is solved. That is, in suitable function spaces, it is shown that for any vacuum space-time near flat space, its mass m is strictly positive. The relationship to other work in the field and some discussion of the global problem is given. Our proof is, in effect, a version of critical point analysis in infinite dimensions, but detailed L^p and Sobolev-type estimates are needed for the precise proof, as well as careful attention to the coordinate invariance group. For the latter, we prove a suitable slice theorem based on the use of harmonic coordinates.
|Additional Information:||© Springer-Verlag 1976. Received: 3 December 1975. Communicated by J. Ehlers. Partially supported by the University of Toronto, Universite de Paris VI and NSF Grant MPS-75-05576. We wish to thank J. Arms, A. Fischer, R. Sachs, A. Taub, A. Tromba and A. Weinstein for several useful remarks.|
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|Deposited By:||Ruth Sustaita|
|Deposited On:||30 Jul 2010 16:50|
|Last Modified:||26 Dec 2012 12:16|
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