  The symmetric two-point function for a massless, minimally coupled scalar
field in the Unruh state is examined for Schwarzschild-de Sitter spacetime in
two dimensions. This function grows linearly in terms of a time coordinate that
is well-defined on the future black hole and cosmological horizons, when the
points are split in the space direction. This type of behavior also occurs in
two dimensions for other static black hole spacetimes when the field is in the
Unruh state, and at late times it occurs in spacetimes where a black hole forms
from the collapse of a null shell. The generalization to the case of the
symmetric two-point function in two dimensions for a massive scalar field in
Schwarzschild-de Sitter spacetime is discussed.
