  We study series of the stationary solutions with asymptotic flatness
properties in the Einstein-Maxwell-free scalar system because they are locally
equivalent with the exterior solutions in some class of the scalar-tensor
theories of gravity. First, we classify spherical exterior solutions into two
types of the solutions, an apparently black hole type solution and an
apparently worm hole type solution. The solutions contain three parameters, and
we clarify their physical significance. Second, we reduce the field equations
for the axisymmetric exterior solutions. We find that the reduced equations are
partially the same as the Ernst equations. As simple examples, we derive new
series of the static, axisymmetric exterior solutions, which correspond to
Voorhees's solutions. We then show a non-trivial relation between the spherical
exterior solutions and our new solutions. Finally, since null geodesics have
conformally invariant properties, we study the local geometry of the exterior
solutions by using the optical scalar equations and find some anomalous
behaviors of the null geodesics.
