On Slowly Rotating Homogeneous Masses in General Relativity

The present paper is devoted to a study of slowly rotating homogeneous masses in which the energy density ∊ is a constant. The structure of such configurations is determined with the aid of equations derived by Hartle in the exact framework of general relativity. These configurations have a natural limit in that the static, non-rotating, configurations must have radii (R) exceeding 9/8 times the Schwarzschild radius (RS). The derived structures, for varying R/RS, are illustrated by a series of graphs. A result of particular interest which emerges is that the ellipticity of the configuration, for varying radius but constant mass and angular momentum, exhibits a very pronounced maximum at R/RS ∼ 2.4.