The bright side of dark matter

We show that it is not possible in the absence of dark matter to construct a four-dimensional metric that explains galactic observations. In particular, by working with an effective potential it is shown that a metric which is constructed to fit Rat rotation curves in spiral galaxies leads to the wrong sign for the bending of light, i.e., repulsion instead of attraction. Hence, without dark matter the motion of particles on galactic scales cannot be explained in terms of geodesic motion on a four-dimensional metric. This reveals that dark matter is indispensable if we wish to retain the cherished equivalence principle.