Isentropic Hydrodynamics in Plane Symmetric Space-Times

Abstract

Use is made of a form of the stress energy tensor of a perfect fluid, previously derived for special relativity, to show that for irrotational isentropic motions a co-moving coordinate system exists in which both sides of the Einstein gravitational field equations may be expressed in terms of the dependent variables of the self-gravitational problem for a perfect fluid. It is shown that for a space-time with plane symmetry the field equations and the assumption of isentropy imply the conservation of mass. General methods for dealing with these field equations are given for the static and spatially independent cases. Approximate solutions are obtained for other specific cases. The general exact solution is obtained for the incompressible case. Properties of the incompressible case are discussed.