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Strongly coupled gravitational systems describe Einstein gravity and matterin the limit that Newton's constant G is assumed to be very large. Thenonlinear evolution of these systems may be solved analytically in theclassical and semiclassical limits by employing a Green function analysis.Using functional methods in a Hamilton-Jacobi setting, one may compute thegenerating functional (`the phase of the wavefunctional') which satisfies boththe energy constraint and the momentum constraint. Previous results areextended to encompass the imposition of an arbitrary initial hypersurface. ALagrange multiplier in the generating functional restricts the initial fields,and also allows one to formulate the energy constraint on the initialhypersurface. Classical evolution follows as a result of minimizing thegenerating functional with respect to the initial fields. Examples are givendescribing Einstein gravity interacting with either a dust field and/or ascalar field. Green functions are explicitly determined for (1) gravity, dust,a scalar field and a cosmological constant and (2) gravity and a scalar fieldinteracting with an exponential potential. This formalism is useful in solvingproblems of cosmology and of gravitational collapse.Comment: 30 pages Latex (IOP) file with 2 IOP style files, to be published in  Classical and Quantum Gravity (1998

Initial hypersurface formulation: Hamilton-Jacobi theory for strongly coupled gravitational systems