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On a Class of Non-Static Perfect Fluid Spheres in General Relativity

The line element given by McVittie [1] for a spherically symmetric distribution of matter is generalized. Conditions which are necessary and sufficient are given for the density to be uniform. The motion of the matter configuration is investigated with a view to oscillations using different physical conditions and initial conditions. It is shown that for many classes of solutions, these conditions are sufficient to conclude that oscillations are not possible. Particularly it is found that for a gasous mass, oscillations are not possible. For other classes of solutions, it is shown that the conditions necessary for the solutions to be physically acceptable, are consistent with oscillations. However, these conditions are in general not sufficient.