  A Green's function method is developed for solving strongly-coupled gravity
and matter in the semiclassical limit. In the strong-coupling limit, one
assumes that Newton's constant approaches infinity. As a result, one may
neglect second order spatial gradients, and each spatial point evolves like an
homogeneous universe. After constructing the Green's function solution to the
Hamiltonian constraint, the momentum constraint is solved using functional
methods in conjunction with the superposition principle for Hamilton-Jacobi
theory. Exact and approximate solutions are given for a dust field or a scalar
field interacting with gravity.
