Searching for MOND in scalar-tensor theories of gravity

Abstract

In this paper, I study spherically symmetric solutions in a simple class of geometric sigma models of the Universe. This class of models is a subclass of the wider class of scalar-tensor theories of gravity. The purpose of this work is to examine how the additional scalar degree of freedom modifies Newtonian gravitational force. The general solution for spherically symmetric metric far from the point source is obtained in a weak field approximation. As it turns out, it is parametrized by the mass of the source, and an additional function of time. One particular model is examined as an example. It is shown that there are solutions that accommodate MOND regime at some distances from the source. Unfortunately, the obtained interval of distances turns out to be smaller than it is needed. An additional analysis shows that genuine MOND, that explains galactic curves of all nearby galaxies, cannot be obtained.