POST-NEWTONIAN OSCILLATIONS OF A ROTATING-DISK OF DUST

At the first post-Newtonian approximation to general relativity, analy tic solutions are presented for the motions of generalized MacLaurin d isks of dust. The main result consists in the solution for a rotating and oscillating disk. This disk has the remarkable property that, in c ontrast with its Newtonian analogue, it is rotating nonuniformly. Even in the stationary limit of a vanishing oscillation amplitude, the rot ation law does not become rigid. On the other hand, by imposing initia lly uniform rotation and nonoscillatory motion, the motion is found in agreement with earlier results by Bardeen and Wagoner. The solution o f the collapsing generalized MacLaurin disk without rotation is presen ted also.