  Within a gauge formulation of 3+1 gravity relying on a nonlinear realization
of the group of isometries of space-time, a natural expansion of the metric
tensor arises and a simple choice of the gravity dynamical variables is
possible. We show that the expansion parameter can be identified with the
gravitational constant and that the first order depends only on a diagonal
matrix in the ensuing perturbation approach. The explicit first order solution
is calculated in the static isotropic case, and its general structure is worked
out in the harmonic gauge.
