Difference between AdS and dS spaces: wave equation approach

Abstract

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.

23 pages, version to appear in CQG

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Cited by in corpus (10)

• Quasinormal modes of D-dimensional de Sitter spacetime
• Dirac quasinormal modes of D-dimensional de Sitter spacetime
• Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime
• Quasinormal modes from potentials surrounding the charged dilaton black hole
• Negative phase velocity of electromagnetic waves and the cosmological constant
• Quasinormal modes and dual resonant states on de Sitter space
• Robin boundary conditions in acoustic BTZ black holes
• Unitarity issue in BTZ black holes
• Quasinormal Modes in Generalized Nariai Spacetimes
• Second Order Perturbative Calculation of Quasinormal Modes of Schwarzschild Black Holes