Newtonian Aspects of General Relativistic Galaxy Models

TL;DR

This paper explores how general relativistic models of galaxies, especially rotating dust solutions, relate to Newtonian and Post-Newtonian gravity, offering insights into galaxy rotation curves without solely relying on dark matter.

Contribution

It analyzes the Newtonian and Post-Newtonian limits of axially symmetric, rotating dust solutions in Einstein's equations, bridging general relativity and classical galaxy models.

Findings

Newtonian limit includes Post-Newtonian terms

Relates relativistic models to classical rotation curves

Provides groundwork for alternative gravity-based explanations

Abstract

Many cosmological observations call for the existence of dark matter. The most direct evidence for dark matter is inferred from the measured flatness of galactic rotation curves. The latter is based on Newtonian gravity. Alternative approaches to the rotation curve problem by means of general relativity have recently been put forward. The class of models of interest is a subset of the axially symmetric and stationary solutions of Einstein's equations with rotating dust. As a step toward the understanding of general relativistic galaxy models, we analyse rigidly as well as non-rigidly rotating (Post-)Newtonian spacetimes. We find that the Newtonian limit of the considered general relativistic galaxy model leads to Post-Newtonian terms in the metric.