Post-Newtonian approximation of the rigidly rotating disc of dust to arbitrary order - art. no. 064012

Using the analytic, global solution for the rigidly rotating disc of dust a s a starting point, an iteration scheme is presented for the calculation of an arbitrary coefficient in the post-Newtonian (PN) approximation of this solution. The coefficients were explicitly calculated up to the 12(th) PN l evel and are listed in this paper up to the 4(th) PN level. The convergence of the series is discussed and the approximation is found to be reliable e ven in highly relativistic cases. Finally, the ergospheres are calculated a t increasing orders of the approximation and for increasingly relativistic situations.