Difference between anti-de Sitter and de Sitter spaces: wave equation approach

We study the wave equation for a massive scalar field in three-dimensional anti-de Sitter (AdS) black hole and de Sitter (dS) spaces to find what are the differences and similarities between the 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, quasi-normal modes are obtained and the AdS/CFT correspondence is confirmed. However, we do not find quasi-normal 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