The interior field of a thin mass shell of arbitrary angular momentum per unit mass -a is examined as a power series in a parameter (V²=1-2m/R+a²R²) which measures the nearness of the shell to its gravitational radius. The exterior field is assumed to be the Kerr metric. Shell shape is arbitrary beyond the requirement of sphericity in the limits a→0 or V→0. It is shown that, as V→0, the interior intertial frames are dragged around rigidly at the same rate as the shell, for all a. A class of shapes is found for which (in the same limit) the interior spacetime becomes completely flat. This generalizes small-a results due to Brill and Cohen and to De La Cruz and Israel. Limits for physically acceptable a are found which correlate with related work by Smarr.
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Lawrence P. Orwig (1978) studied this question.