  We study a thermofield double type entangled state on two disjoint universes
$A$ and $B$, where one of the universes is asymptotically flat containing a
black hole. As we increase the entanglement temperature, this black hole
receives back-reaction from the stress energy tensor of the state. This results
in lengthening of the wormhole region in the black hole interior, and
decreasing of its horizon area, both of which are key features of an
evaporating black hole. We then compute the entanglement entropy on the
universe $A$ through the island formula, and argue that it naturally follows
the Page curve of an evaporating black hole in flat space. We also study the
effects of local operations in the gravitating universe with the black hole. We
find that they accelerate the evaporation of the black hole, therefore disrupt
the entanglement between two universes. Furthermore, we observe that depending
on whether the operation can be regarded as an LOCC or not, the behavior of the
entanglement entropy changes. In particular, when the operation is made neither
in the entanglement wedge of the radiation system or that of the black hole,
the transition between the island phase and the no-island phase can happen
multiple times.
