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We study the possible types of the nucleation of vacuum bubbles. We classifyvacuum bubbles in de Sitter background and present some numerical solutions.The thin-wall approximation is employed to obtain the nucleation rate and theradius of vacuum bubbles. With careful analysis we confirm that Parke's formulais also applicable to the large true vacuum bubbles. The nucleation of thefalse vacuum bubble in de Sitter background is also evaluated. The tunnelingprocess in the potential with degenerate vacua is analyzed as the limitingcases of the large true vacuum bubble and false vacuum bubble. Next, weconsider the pair creation of black holes in the background of bubblesolutions. We obtain static bubble wall solutions of junction equation withblack hole pair. The masses of created black holes are uniquely determined bythe cosmological constant and surface tension on the wall. Finally, we obtainthe rate of pair creation of black holes.

The vacuum bubbles in de Sitter background and black hole pair creation