Notes on wormhole existence in scalar-tensor and F(R) gravity
  Some recent papers have claimed the existence of static, spherically
symmetric wormhole solutions to gravitational field equations in the absence of
ghost (or phantom) degrees of freedom. We show that in some such cases the
solutions in question are actually not of wormhole nature while in cases where
a wormhole is obtained, the effective gravitational constant G_eff is negative
in some region of space, i.e., the graviton becomes a ghost. In particular, it
is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke
theory with zero potential and the coupling constant \omega > -3/2, except for
the case \omega = 0; in the latter case, G_eff < 0 in the region beyond the
throat. The same is true for wormhole solutions of F(R) gravity: special
wormhole solutions are only possible if F(R) contains an extremum at which
G_eff changes its sign.
