  We study the possible types of the nucleation of vacuum bubbles. We classify
vacuum bubbles in de Sitter background and present some numerical solutions.
The thin-wall approximation is employed to obtain the nucleation rate and the
radius of vacuum bubbles. With careful analysis we confirm that Parke's formula
is also applicable to the large true vacuum bubbles. The nucleation of the
false vacuum bubble in de Sitter background is also evaluated. The tunneling
process in the potential with degenerate vacua is analyzed as the limiting
cases of the large true vacuum bubble and false vacuum bubble. Next, we
consider the pair creation of black holes in the background of bubble
solutions. We obtain static bubble wall solutions of junction equation with
black hole pair. The masses of created black holes are uniquely determined by
the cosmological constant and surface tension on the wall. Finally, we obtain
the rate of pair creation of black holes.
