General Relativistic Rotation Curves in a Post-Newtonian Light

TL;DR

This paper investigates whether general relativity, specifically Post-Newtonian approximations of rotating dust solutions, can explain galaxy rotation curves without dark matter, highlighting the necessity of Post-Newtonian terms for physical plausibility.

Contribution

It demonstrates that incorporating Post-Newtonian corrections is essential in relativistic models of galaxy rotation, advancing the understanding of gravity's role in galactic dynamics.

Findings

Post-Newtonian terms are necessary for physical consistency.

Relativistic models can potentially explain rotation curves without dark matter.

Newtonian models are insufficient for accurate galactic rotation modeling.

Abstract

The missing of a Keplerian fall-off in the observed galaxy rotation curves represents classical evidence for the existence of dark matter on galactic scales. There has been some recent activity concerning the potential of modelling galactic systems with the help of general relativity. This was motivated by claims that by the use of full general relativity dark matter could be made superfluous. Here we focus on possible axisymmetric and stationary solutions of Einstein's equations with rotating dust. After a short review of the current debate we pursue the idea of approaching such relativistic models in a Newtonian language. We analyse rigidly as well as differentially rotating Newtonian and Post-Newtonian spacetimes and find that it is necessary to incorporate a Post-Newtonian term in order to make physical sense.