Difference between AdS and dS spaces: wave equation approach

TL;DR

This paper compares wave equations in three-dimensional AdS-black hole and dS spaces, analyzing their horizons, quasinormal modes, and holographic correspondences to understand their similarities and differences.

Contribution

It provides the first detailed comparison of wave equations and quasinormal modes in AdS and dS spaces, clarifying their holographic dualities and global structure differences.

Findings

Quasinormal modes are obtained for AdS-black hole but not for dS space.

AdS/CFT correspondence is confirmed, dS/CFT remains unconfirmed.

Differences in global structure influence the presence of quasinormal modes.

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.