  In this paper, we provide a counter-example to the ER=EPR conjecture. In an
anti-de Sitter space, we construct a pair of maximally entangled but separated
black holes. Due to the vacuum decay of the anti-de Sitter background toward a
deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are
reasonably large, then within the scrambling time, there should appear an
Einstein-Rosen bridge between the two black holes. Now by tracing more details
on the bubble dynamics, one can identify parameters such that one of the two
bubbles either monotonically shrinks or expands. Because of the change of
vacuum energy, one side of the black hole would evaporate completely. Due to
the shrinking of the apparent horizon, a signal of one side of the
Einstein-Rosen bridge can be viewed from the opposite side. We analytically and
numerically demonstrate that within a reasonable semi-classical parameter
regime, such process can happen. Bubbles are a non-perturbative effect, which
is the crucial reason that allows the transmission of information between the
two black holes through the Einstein-Rosen bridge, even though the probability
is highly suppressed. Therefore, the ER=EPR conjecture cannot be generic in its
present form and its validity maybe restricted.
