The Stability of a Spherically Symmetric Cluster of Stars Describing Circular Orbits

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Abstract
Some general properties are derived for a stationary system of many gravitating masses of a type described by Einstein some years ago. The system is assumed to give the average field and the average density of matter for a globular cluster of stars. It is shown that a particularly smooth join of the field within the cluster to the exterior field in free space can be made when the density of matter tends to zero at the boundary. Also the condition for the stability of the masses in their orbits is shown to place an upper limit to their velocities, which in most cases restricts the gravitational mass of the cluster to a value which is less than its rest mass.

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