  Recently, it was hypothesized that some supermassive black holes (SMBHs) may
couple to the cosmic expansion. The mass of these SMBHs increase as the cubic
power of the cosmic scale factor, leaving the energy density of the SMBHs
unchanged when the universe expands. However, following general principles of
general relativity, namely, locality or junction conditions, we show that the
inner part of a gravitationally bounded system is unaware of the cosmic
expansion, since the outer solution can be smoothly replaced by an
asymptotically flat background. For the same reason, the direct reason that we
do not expand with the expansion of the universe is not that we are bound
states, but rather we are positioned in a greater gravitationally bounded
system, namely the local group.
