A generalization of the concept of constant mean curvature and canonical time.
Abstract
Some compact spaces of achronal hypersurfaces are constructed in various types of spacetime. A variational principle is introduced on these spaces, smooth extremals of which are spacelike hypersurfaces of constant mean curvature. The integrand of the variational principle is shown to be upper semicontinuous and the direct methods of the calculus of variations are applied to obtain aC ^{0} extremal, which is defined to be a spacelike hypersurface of generalized constant mean curvature. The family of such hypersurfaces generated by altering the value of the mean curvature is discussed and the mean curvature itself is shown to have many of the properties of a canonical time coordinate.
 Publication:

General Relativity and Gravitation
 Pub Date:
 July 1977
 DOI:
 10.1007/BF00762636
 Bibcode:
 1977GReGr...8..525G
 Keywords:

 Curvature;
 Relativity;
 SpaceTime Functions;
 Canonical Forms;
 Functionals;
 Hyperplanes;
 Variational Principles;
 Astrophysics