Previous work on approximate solutions for rotating mass shells with flat interior is extended to third order in the angular velocity omega . It is shown that the condition of flatness can only be preserved in this order if the mass shell exhibits differential rotation. The first-order result, that a compact rotating mass shell with M=2R creates total dragging of the inertial frames inside the shell, is not invalidated by third-order corrections. By analysing the structure of the solutions in arbitrary order of omega , it is proven that there exists exactly one solution for a rotating mass shell with flat interior.
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Pfister et al. (1986) studied this question.
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