  We study 4-dimensional Schwarzschild de Sitter black holes in the regime
where the black hole mass is small compared with the de Sitter scale. Then the
de Sitter temperature is very low compared with that of the black hole and we
study the black hole, approximating the ambient de Sitter space as a frozen
classical background. We consider distant observers in the static diamond, far
from the black hole but within the cosmological horizon. Using 2-dimensional
tools, we find that the entanglement entropy of radiation exhibits linear
growth in time, indicative of the information paradox for the black hole.
Self-consistently including an appropriate island emerging at late times near
the black hole horizon leads to a reasonable Page curve. There are close
parallels with flat space Schwarzschild black holes in the regime we consider.
