The variational principle in the general theory of relativity

It is pointed out that the Hilbert Lagrangian in the general theory of relativity (the scalar of the curvature) is not characteristic for the boundary value problem for Einstein's equations in view of its linearity with respect to the leading derivative of the metric. This is due to the fact that for the boundary term in the variation of the action to vanish it is necessary to specify additional boundary conditions which contradict the order of Einstein's equations. This is illustrated with an example from mechanics. The characteristic Lagrangian for Einstein's equations is the "truncated" Dirac Lagrangian (following from the guage approach to the general theory of relativity), operation with which is similar to the addition to the Hilbert Lagrangian of a "boundary term" (as was assumed by Gibbons and Hawking). The need for this addition is pointed out.