Vacuum bubbles in a de Sitter background and black hole pair creation

Abstract

We study the possible types of nucleation of vacuum bubbles. We classify vacuum bubbles in a 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 a 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 the static bubble wall solutions of the junction equation with a black hole pair. The masses of created black holes are uniquely determined by the cosmological constant and the surface tension on the wall. Finally, we obtain the rate of pair creation of black holes.