Can galactic observations be explained by a relativistic gravity theory?

We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression for the metric to order (v/c)2. This allows us to compare the predictions of the theory with various experimental data: the Newtonian limit, light deflection and retardation, rotation of galaxies and gravitational lensing. Our general conclusion is that the possibility for any gravity theory to explain the behaviour of galaxies without dark matter is rather improbable. PACS numbers: 04.50.+h, 04.25.Nx, 95.35.+d Typeset using REVTEX 1 Einstein’s gravity theory and some other alternative gravity models are in good agreement with the experimental data in the solar system and the laboratory [1]. However, the behavior of galactic systems poses a great challenge to gravity theories. For virtually all spiral galaxies the tangential rotational velocity curves tend toward some constant value. This fact is in sharp contradiction with the visible star (luminosity) distribution and the laws of Newtonian dynamics. The stars in the outer parts of galaxies rotate several times faster than predicted by the standard gravity theory. A similar problem is observed in gravitational lensing [2]. Just as in the solar system problems of the past century (concerning the orbits of Uranus and Mercury), there are two ways to resolve these difficulties. One, the most widely adopted, is the dark matter hypothesis [3]. It is presumed that the visible stars are imbedded in a massive nearly spherical halo of nonluminous matter. The mass of the halo varies from one galaxy to another but generally it constitutes about 90% of the total mass. This hypothesis explains the flat rotational curves of galaxies. Yet it has its own troubles, in particular (i) no good model for the formation of the dark halo is known, and (ii) after much effort and many proposals no known form of matter has yet given a satisfactory model for the massive halo. (The few recently observed cases of gravitational microlensing [4] are as yet far from conclusive evidence for the dark matter explanation). The second way is to assume that for galactic distances Newton’s gravity law is no longer valid. This possibility has also been the subject of some discussions [5–8]. In particular it was shown [9] that a modified gravitational potential of the form