Parametrization of the Space of Solutions of Einstein's Equations
- 23 November 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 59 (21) , 2389-2392
- https://doi.org/10.1103/physrevlett.59.2389
Abstract
An explicit parametrization is obtained of the set of all space-time solutions of Einstein's equations which are globally hyperbolic and contain a compact spatial hypersurface with constant mean curvature. This parametrization is based upon the conformal treatment of the initial-value problem for Einstein's equations, which is studied by the method of sub and super solutions for quasilinear elliptic partial differential equations. The Yamabe-Aubin-Trudinger-Schoen classification of conformal classes of Riemannian metrics plays a key role.Keywords
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