Can General Relativity play a role in galactic dynamics?

TL;DR

This paper explores how weak-field general relativity, specifically gravitomagnetic effects, could significantly influence galactic rotation curves, challenging the traditional Newtonian perspective.

Contribution

It demonstrates that homogeneous solutions of the gravitomagnetic field can produce notable corrections to galactic velocity profiles, linking general relativity to galactic dynamics.

Findings

Homogeneous gravitomagnetic solutions can affect galactic rotation curves.

General relativity may provide alternative explanations for galactic dynamics.

Non-negligible relativistic corrections are possible in weak-field regimes.

Abstract

We use the gravitoelectromagnetic approach to the solutions of Einstein's equations in the weak-field and slow-motion approximation to investigate the impact of General Relativity on galactic dynamics. In particular, we focus on a class of the solutions for the gravitomagnetic field, and show that, contrary to what is expected, they may introduce non negligible corrections to the Newtonian velocity profile. These are the homogeneous solutions (HS) for the gravitomagnetic field, i.e. solutions with vanishing matter currents. We show how recent results about galactic dynamics are connected to this class of solutions.