Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-01-15
Class.Quant.Grav.24:1055-1068,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages, uses document class iopart, v2: minor corrections
Scientific paper
10.1088/0264-9381/24/5/003
The scheme developed by Hartle for describing slowly rotating bodies in 1967 was applied to the simple model of constant density by Chandrasekhar and Miller in 1974. The pivotal equation one has to solve turns out to be one of Heun's equations. After a brief discussion of this equation and the chances of finding a closed form solution, a quickly converging series solution of it is presented. A comparison with numerical solutions of the full Einstein equations allows one to truncate the series at an order appropriate to the slow rotation approximation. The truncated solution is then used to provide explicit expressions for the metric.
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