Rigid rotation in GR and a generalization of the virial theorem

TL;DR

This paper explores rigidly rotating dust solutions in general relativity, comparing them to special relativity cases, and introduces a generalized virial theorem that could impact dark matter estimates in galaxies.

Contribution

It introduces a general relativistic model of rigid rotation and derives a generalized virial theorem for stationary spacetimes, with implications for galactic dark matter.

Findings

No Doppler effect in the relativistic rigid body model

Generalized virial theorem includes non-Newtonian contributions

Potential re-weighting of dark matter in galaxies

Abstract

In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a rigid body in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the rigid body. This effect can be important to test the validity of the assumed model for our galaxy. In the second part we approach the problem from a low energy expansion perspective and we write down a generalization of the virial theorem for stationary spacetimes. The non-Newtonian contributions can lead to a re-weighting of dark matter in galaxies.