Topological constraints on general relativistic galaxy modelling

Abstract We study the impact on the average rotational dynamics and gravitational lensing of topological structures within fully general relativistic galaxy models. These topological structures do not possess a Newtonian analogue and, therefore, represent a purely general relativistic feature which could a priori impact galactic observables. We characterise these structures both for rigidly rotating and differentially rotating solutions. By employing GAIA DR3 data, we find that such topological defects can impact the transition between the rising and flat regimes of the galaxy. Furthermore, we show that topological defects produce a noticeable increase in the deflection angle produced by Milky Way-like galaxies. Finally, we find that topological singularities can be avoided within the class of differentially rotating solutions.