Gravitational collapse of spherical shells of fluid in the isotropic
  homogeneous universe
  We investigate gravitational collapse of thick shell of fluid in the
isotropic homogeneous universe without radiation described by the Einstein
gravity with cosmological constant. We construct analytic solutions of this
kind interpolating the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and
the de-Sitter Schwarzschild black hole one by the Gullstrand-Painlev\'e one.
After determining the scale factor for a perfect fluid coexisting with
cosmological constant, we determine the orbit of the collapsing shells of fluid
from the continuity condition for density and the perpendicular component of
pressure at interface. However the continuity condition cannot fix the orbit
when there does not exist a perfect fluid inside the shells. In this case we
determine the orbit from an equation of state for the fluid consisting a shell
near the surface. Finally we confirm that the total energy defined in
arXiv:2005.13233 is independent of the given time evolution in this system.
