  There are several exotic tunneling processes that can be realized only by
incorporating the effect of gravity. Here, we point out that we encounter
difficulties in constructing the WKB wave function, once we try to describe
quantum fluctuations around the semi-classical tunneling path. We present
examples of pathology in the true vacuum decay/upward tunneling, the false
vacuum decay catalyzed by a black hole and the tunneling with black
hole/wormhole production.
