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Solving the Hamilton-Jacobi equation for gravitationally interacting electromagnetic and scalar fields

B. K. Darian
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Abstract

The spatial gradient expansion of the generating functional was recently developed by Parry, Salopek, and Stewart to solve the Hamiltonian constraint in Einstein-Hamilton-Jacobi theory for gravitationally interacting dust and scalar fields. This expansion is used here to derive an order-by-order solution of the Hamiltonian constraint for gravitationally interacting electromagnetic and scalar fields. A conformal transformation and functional integral are used to derive the generating functional up to the terms fourth order in spatial gradients. The perturbations of a flat Friedmann-Robertson-Walker cosmology with a scalar field, up to second order in spatial gradients, are given. The application of this formalism is demonstrated in the specific example of an exponential potential.

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B. K. Darian. 1997-09-27. Solving the Hamilton-Jacobi equation for gravitationally interacting electromagnetic and scalar fields. https://doi.org/10.1088/0264-9381%2F15%2F1%2F010

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