Slowly Rotating Homogeneous Stars and the Heun Equation

Abstract

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.

arXiv comment16 pages, uses document class iopart, v2: minor corrections

References in corpus (7)

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Cited by in corpus (6)

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• Slowly rotating Tolman VII solution
• Symbolic analysis of second-order ordinary differential equations with polynomial coefficients
• Confluent Heun functions and the Coulomb problem for spin 1/2 particle in Minkowski space