Parametrization of the space of solutions of Einstein's equations

Details Parametrization of the space of solutions of Einstein's equations Parametrization of the space of solutions of Einstein's equations

Nov 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvl..59.2389i&link_type=abstract

Physical Review Letters, Volume 59, Issue 21, November 23, 1987, pp.2389-2392

Physics

13

Exact Solutions

Scientific paper

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.

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