Just dust : About the (in)applicability of rotating dust solutions as realistic galaxy models

TL;DR

This paper examines rotating dust solutions in Einstein's equations to assess their suitability as realistic galaxy models, concluding they are generally unphysical or inadequate for such purposes.

Contribution

It demonstrates the limitations of stationary axisymmetric rotating dust solutions as global galaxy models, highlighting issues with their physical plausibility.

Findings

Interior solutions become unphysical in certain regions

Rigid rotation solutions cannot be extended into vacuum

Non-rigid rotation solutions are also generally inadequate

Abstract

Solutions of the stationary axisymmetric Einstein equations describing the interior of circularly rotating dust are investigated in order to study their potential applicability as galaxy models. It is shown that such interior solutions cannot be used as global metrics without becoming unphysical in certain regions of space. Although definite results concerning the non-existence of a continuation into a vacuum can only be derived for interior solutions describing rigidly rotating dust, the present analysis exhibits that the case of non-rigidly rotating dust would in general also be inadequate as a physically reasonable galaxy model.