The study of frame dragging by massive rotating spherical shells has been of interest in the context of Mach's principle. The Lense-Thirring effect is a well-known post-Newtonian solution that is limited to relatively small masses. Brill and Cohen wrote a well-known paper that applies to arbitrarily large masses and relatively small angular velocities. A summary of their results is given here. I have some questions about this paper.
One would expect that as the mass of the rotating shell goes to infinity, the inertial frames inside the shell would rotate at the same angular velocity. From the formulas linked above however, as the mass goes to infinity, beta goes to -0.5 and the angular velocity of the inertial frames goes to 4 times the angular velocity of the shell (note that alpha=m/2). This seems odd, can anyone explain this?
The authors make a continuity assumption of the metric across the thin spherical surface. Why is that? If the mass goes to infinity, one expects discontinuities, as inside the shell the metric is approximately flat while the external metric could be that of a massive black hole.
The authors use a model assumption inspired by the Lense-Thirring result that stating that the angular velocity of inertial frames inside the shell depends on the radius r. Is there any justification for copying the result of a post-Newtonian analysis as a valid assumption for a non-post-Newtonian analysis?
Weinberg discusses the matter in Gravitation and Cosmology section 9.7.
