We numerically study the dynamics of false vacuum bubbles which are inside
an almost flat background; we assumed spherical symmetry and the size of the bubble is
smaller than the size of the background horizon. According to the thin shell approximation
and the null energy condition, if the bubble is outside of a Schwarzschild black hole, unless
we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible.
In this paper, we extend our method to beyond the thin shell