  We study the wave equation for a massive scalar field in three-dimensional
AdS-black hole and dS (de Sitter) spaces to find what is the difference and
similarity between two spaces. Here the AdS-black hole is provided by the J=0
BTZ black hole. To investigate its event (cosmological) horizons, we compute
the absorption cross section, quasinormal modes, and study the AdS(dS)/CFT
correspondences. Although there remains an unclear point in defining the
ingoing flux near infinity of the BTZ black hole, quasinormal modes are
obtained and the AdS/CFT correspondence is confirmed. However, we do not find
quasinormal modes and thus do not confirm the assumed dS/CFT correspondence.
This difference between AdS-black hole and dS spaces is very interesting,
because their global structures are similar to each other.
