Solution of the local mass problem in general relativity
Choquet-bruhat, Y. and J. E. Marsden
Comm. Math. Phys., 51, (1976), 283-296
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 Lp
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.
