Rotating Masses and Their Effect on Inertial Frames

An analysis is given of the stress-energy tensor and geometry produced by slowly rotating bodies. The geometrized mass $\frac{\mathrm{GM}}{c^2}$ of the body is allowed to be comparable to its radius. The geometry is treated as a perturbation of the Schwarzschild geometry, which leads to considerable simplification of Einstein's equations. The rotation of the intertial frame induced by a rotating massive shell is calculated and discussed with particular attention to two limiting cases: (1) For small masses it reduces to Thirring's well-known result; (2) for large masses, whose Schwarzschild radius approaches the shell radius, the induced rotation approaches the rotation of the shell. These and the corresponding results for an expanding and recollapsing dust cloud are examined for their consistency with particular interpretations of Mach's principle. The analytic extension of the rotating exterior metric is a completely source-free rotating solution. It describes a slowly rotating, expanding, and recontracting Einstein-Rosen bridge which can be taken as a geometrodynamic model for a slowly rotating body.