Re-weighting dark matter in disc galaxies: a new general relativistic observational test

Abstract

A recent analysis of data from the ESA Gaia mission demonstrated that the kinematics of stars in the Milky Way can be modelled without invoking the presence of dark matter whatsoever. Indeed, the higher-than-Keplerian velocities observed in outer stars can be ascribed to the properties of the general relativistic (GR) metric assumed to describe the Galaxy. Here we generalize the concept, and derive the most general exact GR model for a stationary axi-symmetric dynamically cold dust structure. We explicitly show how deviations from the commonly adopted Newtonian dynamics are indeed manifest even at low velocities and low densities. We provide for the first time a detailed description of the frequency shift experienced by photons travelling from any emission site within an external disc galaxy to the observer, relating the outcome of the shift measurement to the gravitational properties of the galaxy. Finally, we devise a novel, groundbreaking observational test potentially able to fully characterize the GR metric under the minimal set of assumptions mentioned above. The proposed experiment exploits the effects non-diagonal GR terms have on the frequency shift of photons, ultimately providing a test to evaluate whether dark matter is actually required by disc galaxy kinematics.

Galactic dark matter effects from purely geometrical aspects of General Relativity

“…Let us now compare the accepted special relativistic description (SR), which accounts only for the kinematic Doppler shift, to the general relativistic description (GR), which instead includes the gravitational shift effect. The expressions for the redshift for the model that we are considering were calculated by Astesiano et al [23], and read:…”

Pitfalls in applying gravitomagnetism to galactic rotation curve modelling

“…They found that the Milky Way's rotation curve was equally well fit by both. The model was generalized by Astesiano et al [4,5], who again found that a purely GR analysis, without dark matter, could account for the observations. In the studies of Astesiano and Ruggiero [6] (hereafter AR22) and [7], the specific role of the post-Newtonian gravitomagnetic effect was made clear in these 'GR without Dark Matter' models.…”