The interior solution of axially symmetric, stationary and rigidly rotating dust configurations

TL;DR

This paper demonstrates that the interior solutions for axially symmetric, stationary, rigidly rotating dust are fully determined by axial mass density, revealing the non-existence of homogeneous dust configurations and exploring cylindrical symmetry cases.

Contribution

It provides a complete characterization of interior solutions based on axial mass density and proves the non-existence of homogeneous dust configurations.

Findings

Interior solutions depend solely on axial mass density.

Homogeneous dust configurations do not exist.

Cylindrical symmetry in mass density is analyzed.

Abstract

It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.