X iv : g r - qc / 9 90 51 01 v 1 2 7 M ay 1 99 9 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 flat 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 a new bright side to dark matter: it is indispensable if we wish to retain the cherished equivalence principle. It has been known for over sixty years, since the work of Zwicky [1] in the early 1930s, that there are significant discrepancies between the luminous and dynamical mass in large astronomical systems such as galaxies and clusters of galaxies. The luminous mass in galaxies is considerably less than the dynamical mass inferred from applying Newtonian gravity to the motion of gas and stars orbiting the galaxies. In clusters of galaxies the luminous mass is again considerably less than the dynamical mass inferred from applying the virial theorem to the motion of the galaxies (keeping in mind that correctly applying the virial theorem depends on whether the clusters are received an “honorable mention” in the 1999 Gravity Research Foundation Essay Competition. E-mail: [email protected]