Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 1976 | public
Journal Article

Solution of the Local Mass Problem in General Relativity

Abstract

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.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023