On some geometric features of the Kramer interior solution for a rotating perfect fluid

TL;DR

This paper investigates the geometric properties of the Kramer interior solution for a rotating perfect fluid, demonstrating that Newtonian convexity properties are preserved despite complex surface features, through analysis of spatial geodesics.

Contribution

It introduces a family of geodesics that generalize Newtonian straight lines and shows that convexity properties hold in the relativistic interior solution.

Findings

Newtonian convexity properties hold for the interior solution

A new family of geodesics generalizes Newtonian straight lines

Geometric analysis confirms convexity despite non-Newtonian surface features

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.