The Post-Newtonian Maclaurin Spheroids to Arbitrary Order

Details The Post-Newtonian Maclaurin Spheroids to Arbitrary Order The Post-Newtonian Maclaurin Spheroids to Arbitrary Order

2003-09-03

arxiv.org/abs/gr-qc/0309017v2

Phys.Rev. D68 (2003) 104029

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 3 figures

Scientific paper

10.1103/PhysRevD.68.104029

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.

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