  This two-part contribution to the Proceedings of the Eighth Canadian
Conference on General Relativity and Relativistic Astrophysics is devoted to
the evolution of a massless scalar field in two black-hole spacetimes which are
not asymptotically flat.
  In Part I (authored by Eric Poisson) we consider the evolution of a scalar
field propagating in Schwarzschild-de Sitter spacetime. The spacetime possesses
a cosmological horizon in addition to the usual event horizon. The presence of
this new horizon affects the late-time evolution of the scalar field.
  In part II (authored by William G. Laarakkers) we consider the evolution of a
scalar field propagating in Schwarzschild-Einstein-de Sitter spacetime. The
spacetime has two distinct regions: an inner black-hole region and an outer
cosmological region. Early on in the evolution, the field behaves as if it were
in pure Schwarzschild spacetime. Later, the field learns of the existence of
the cosmological region and alters its behaviour.
