Motion of a test body in the presence of an external scalar field which   respects the weak equivalence principle
  It is shown that the main contribution to the rotational curve of a spiral galaxy may be due essentially to the interaction, in the general relativistic spacetime, of the galactic matter with a very light long range scalar field which respects the weak equivalence principle. The comparison of the theoretical results with 23 spiral galaxy rotation curves shows a good agreement between our proposal and observations. 
J. P. Mbelek