The Post-Newtonian Maclaurin Spheroids to Arbitrary Order
arXiv:gr-qc/0309017 · doi:10.1103/PhysRevD.68.104029
Abstract
In this paper, we develop an iterative scheme to enable the explicit calculation of an arbitrary post-Newtonian order for a relativistic body that reduces to the Maclaurin spheroid in the appropriate limit. This scheme allows for an analysis of the structure of the solution in the vicinity of bifurcation points along the Maclaurin sequence. The post-Newtonian expansion is solved explicitly to the fourth order and its accuracy and convergence are studied by comparing it to highly accurate numerical results.
31 pages, 3 figures
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- Normal gravity field in relativistic geodesy
- Uniformly Rotating Homogeneous Rings in post-Newtonian Gravity