Cosmological fluids as time variables in general relativity

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Abstract
The use of potentials describing perfect fluids illuminates the role of time in general relativity. Using Hamilton-Jacobi methods, one can find solutions for inhomogeneous situations of interest to cosmology without making an explicit time choice until the very end of the calculation. We compute exact general solutions of long-wavelength matter and radiation interacting with gravity. Hamilton-Jacobi methods can describe adiabatic and isothermal fluctuations as well as the scalar, vector, and tensor modes.