Canonical formulation of the theory of gravitation and a general-covariant separation of space and time

A general-covariant separation of space and time is used to divide four-dimensional space into a family of spacelike hypersurfaces. The operation of differentiatiomvith respect to the parameter t, which numbers the hypersurfaces, is introduced as a Lie derivative along the congruence of the timelike nonunit vector {Mathematical expression}. This method is applied to the variational principle for the gravitational field and is used to construct the corresponding canonical formalism. © 1978 Plenum Publishing Corporation.