  We study a vacuum polarization effect in the background of certain dilatonic
extremal black hole, known as the cornucopion. Whenever the charged fermions
are of any finite mass, the gravitational backreaction to a generic value of a
$CP$ nonconserving vacuum angle $\theta$ is shown to be important owing to a
vacuum energy density which does not vanish deep inside the cornucopion. When
this energy density is positive, this effect creates an extremal horizon at
finite physical distance, closing off the infinite neck. We study the geometry
near this horizon in some detail and find different physical interpretations
for small and large fermion mass. Also, we argue that the conclusion is
qualitatively correct despite the strong coupling.
