Non-Newtonian effects of general relativistic disc galaxy models

Abstract: Galaxy dynamics have long been understood within the framework of Newtonian mechanics, where the low velocities and weak gravitational fields suggest that Einstein’s general relativity (GR) plays only a minor role. However, the struggle to explain the nearly flat rotation curves in disc galaxies historically called for the invocation of dark matter (DM), a non-baryonic matter component that has not yet been detected directly. Even though DM also plays a central role in the ΛCDM cosmological model, its elusive nature has motivated alternative explanations, including Modified Newtonian Dynamics (MOND) and MOdified Gravity theories (MOGs). Nevertheless, GR itself offers a compelling alternative due to the non-linear nature of the Einstein Equations (EE) and the additional degrees of freedom it introduces. Among the most significant effects these features give rise to frame dragging, which becomes particularly relevant in extended, rotating systems. The Balasin-Grumiller (BG) model exemplifies this approach, offering an exact solution of the EE for a stationary, axisymmetric spacetime describing a rigidly rotating disc of dust. Using Zero Angular Momentum Observers (ZAMOs), this model reproduces flat rotation curves and suggests a reduced DM requirement. The choice of observer in GR is crucial for connecting theoretical predictions with measurable quantities, since different reference frames can yield distinct interpretations of stellar motions. For example, analyzing a satellite traversing a general relativistic galaxy requires constructing a locally inertial coordinate system (a laboratory frame) to accurately study how the galaxy appears in such a reference frame. Although restricted to regions outside the bulge and near the galactic plane, dust models highlight how GR can play a crucial role in understanding galaxy dynamics. Thus, it is important to understand to what extent the nonlinearity of general relativity can lead to a discrepancy with Newtonian gravity on large scales, under non-relativistic conditions. A notable feature of the general relativistic models of galaxies is the prediction of Asymptotically Conically Minkowskian (ACM) spacetimes, characterized by a locally flat but conical geometry at large distances. the presence of a topological defect, which is distinct from a curvature singularity, can provide observable signatures that are absent in Newtonian models. Potential tests for ACM structures include: (1) analyzing the holonomy group via the parallel transport of a test vector around the symmetry axis, (2) evaluating how gravitational lensing is affected by angular deficits, and (3) examining scalar field propagation to detect potential ambiguities in vacuum state definitions. Such effects underline the non-Newtonian nature of GR solutions and offer promising avenues for validating these models through astrophysical observations.