  Static (not stationary) solutions of the Einstein-Klein-Gordon (EKG)
equations including matter are obtained for real scalar fields. The scalar
field interaction with matter is considered. The introduced coupling allows the
existence of static solutions in contraposition with the case of the simpler
EKG equations for real scalar fields and gravity. Surprisingly, when the
considered matter is a photon-like gas, it turns out that the gravitational
field intensity at large radial distances becomes nearly a constant, exerting
an approximately fixed force to small bodies at any distance. The effect is
clearly related with the massless character of the photon-like field. It is
also argued that the gravitational field can generate a bounding attraction,
that could avoid the unlimited increase in mass with the radius of the obtained
here solution. This phenomenon, if verified, may furnish a possible mechanism
for explaining how the increasing gravitational potential associated to dark
matter, finally decays at large distances from the galaxies. A method for
evaluating these photon bounding effects is just formulated in order to be
further investigated.
