On slowly rotating homogeneous masses in general relativity

Abstract

The present paper is devoted to a study of slowly rotating homogeneous masses in which the energy density E 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 (R_s). The derived structures, for varying R/R_s, 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/R_s~2.4.