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Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems

D. S. Salopek
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Abstract

Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and semiclassical limits by employing a Green function analysis. Using functional methods in a Hamilton-Jacobi setting, one may compute the generating functional (`the phase of the wavefunctional') which satisfies both the energy constraint and the momentum constraint. Previous results are extended to encompass the imposition of an arbitrary initial hypersurface. A Lagrange multiplier in the generating functional restricts the initial fields, and also allows one to formulate the energy constraint on the initial hypersurface. Classical evolution follows as a result of minimizing the generating functional with respect to the initial fields. Examples are given describing Einstein gravity interacting with either a dust field and/or a scalar field. Green functions are explicitly determined for (1) gravity, dust, a scalar field and a cosmological constant and (2) gravity and a scalar field interacting with an exponential potential. This formalism is useful in solving problems of cosmology and of gravitational collapse.

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D. S. Salopek. 1998-11-24. Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems. https://doi.org/10.1088/0264-9381%2F16%2F1%2F022

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