On a Class of Non-Static Fluid Spheres without Energy Flow

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Abstract
In order to find some common features of relativistic fluid spheres without energy flow, the velocity field in the fluid spheres is examined from the standpoint of its covariant decomposition. The examination shows that, if the velocity field is shear-free, its 4-divergence depends only on time and the converse is also true. It is also shown that the fluid spheres without energy flow dealt with recently by McVittie, Thompson and Whitrow, Bonnor and Faulkes, Bondi and the author are all shear-free.

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