  The general theory of relativity (GR) is symmetric under smooth coordinate
transformations, also known as diffeomorphisms. The general coordinate
transformation group has a linear subgroup denoted as the Lorentz group of
symmetry, which is also maintained in the weak field approximation to GR. The
dominant operator in the weak field equation of GR is thus the d'Alembert
(wave) operator, which has a retarded potential solution. 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 paper, 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.
