Abstract
The scheme developed by Hartle in 1967 for describing slowly rotating bodies 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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