Black hole event horizons are cosmologically coupled

It is shown that an exactly static and spherically symmetric black hole event horizon cannot be embedded in a time-dependent geometry. Forcing it to do so results in a naked null singularity at the would-be horizon. Therefore, since the universe is expanding, black holes must couple to the cosmological expansion, which was suggested as the growth mechanism for supermassive black holes in galaxies, with implications for the dark energy puzzle.