Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later.

Those retardation effects are neglected in the present-day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this presentation, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.

In a previous paper (Asher Yahalom "Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion ‎and Mechanisms Leading to Galactic Rotation Curves" Symmetry 2020, 12(10), 1693; https://doi.org/10.3390/sym12101693) we have shown how the weak approximation to general relativity leads to a d'Alembert wave operator equation for the linear correction to the metric which has a well-known retarded solution and thus retardation arises in the general relativistic analysis.

It should be stressed that the current approach does not require that velocities are high; in fact, most galactic bodies (stars, gas) are substantially subluminal.