On some geometric features of the Kramer interior solution for a rotating perfect fluid
arXiv:gr-qc/9909048 · doi:10.1088/0264-9381/16/12/305
Abstract
Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian features of the bounding surface for some rotation rates, we show, by means of a detailed analysis of the three-dimensional spatial geodesics, that the standard Newtonian convexity properties do hold. A central role is played by a family of geodesics that are introduced here, and provide a generalization of the Newtonian straight lines parallel to the axis of rotation.
LaTeX, 15 pages with 4 Poscript figures. To be published in Classical and Quantum Gravity