Bubble collision with gravitation
  In this paper, we study vacuum bubble collisions with various potentials
including gravitation, assuming spherical, planar, and hyperbolic symmetry. We
use numerical calculations from double-null formalism. Spherical symmetry can
mimic the formation of a black hole via multiple bubble collisions. Planar and
especially hyperbolic symmetry describes two bubble collisions. We study both
cases, when two true vacuum regions have the same field value or different
field values, by varying tensions. For the latter case, we also test symmetric
and asymmetric bubble collisions, and see details of causal structures. If the
colliding energy is sufficient, then the vacuum can be destabilized, and it is
also demonstrated. This double-null formalism can be a complementary approach
in the context of bubble collisions.
