Comments on the static spherically symmetric cosmologies of Ellis, Maartens, and Nel

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Abstract
Ellis, Maartens, and Nel have discussed the viability of static spherically symmetric (SSS) cosmologies in general relativity, and in doing so they have studied some of the mathematical aspects of the field equations in that situation. We investigate further these mathematical aspects. Since the field equations correspond to those studied for stellar models, this question is related to previous investigations in that context. In particular, it is shown that conditions at the center of symmetry do not always uniquely determine the space-time geometry; this has relevance to the numerical investigation of stellar systems. Finally, in view of the need to generalize SSS models, some remarks are made on the possibility of relaxing the staticity condition in the case of models that are shear-free.

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