Mannheim's linear potential in conformal gravity
  We study the equations of conformal gravity, as given by Mannheim, in the
weak field limit, so that a linear approximation is adequate. Specializing to
static fields with spherical symmetry, we obtain a second-order equation for
one of the metric functions. We obtain the Green function for this equation,
and represent the metric function in the form of integrals over the source.
Near a compact source such as the Sun the solution no longer has Schwarzschild
form. Using Flanagan's method of obtaining a conformally invariant metric
tensor we attempt to get a solution of Schwarzschild type. We find, however,
that the 1/r terms disappear altogether. We conclude that a solution of
Mannheim type cannot exist for these field equations.
