Approximate Solutions of the Einstein Equations for Isentropic Motions of Plane-Symmetric Distributions of Perfect Fluids

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Abstract
An approximation procedure is developed and applied to the problem of determining the gravitational and hydrodynamical fields associated with a plane-symmetric distribution of a perfect fluid with arbitrary caloric equation of state in isentropic motion. Special relativistic hydrodynamics in co-moving coordinates are discussed and methods are given for solving specific problems. These solutions provide a zero-order approximation of the corresponding general relativistic problems. The linear equations describing the higher order corrections are discussed and the application of the method of characteristics is pointed out. The existence of shock waves in special relativity makes plausible their existence in general relativity, and they may be used to avoid using physically unacceptable solutions of the field equations.