Quasinormal modes of d-dimensional spherical black holes with a near extreme cosmological constant

Recent observational results suggest that the universe in large scale is described by an Einstein equation with an (at least effective) cosmological constant. In this context, the dynamics of fields in spacetimes which are not asymptotically flat has taken on new importance. Quasinormal modes are a fundamental part of this dynamics. In general, perturbations in the spacetime exterior of a black hole are followed by oscillations which decay exponentially in time. Roughly speaking, these are quasinormal modes, complex frequency modes which carry information about the background geometry, and are independent of the initial perturbation. The characterization of the quasinormal modes originated from compact objects are of particular relevance in gravitational wave astronomy [1]. Their detection is expected to be realized through gravitational wave observations in the near future. In asymptotically anti-de Sitter spacetimes, the antide Sitter/conformal field theory (AdS/CFT) correspondence [2] plays a very important role. In this framework, a link is established among the quasinormal frequencies of a test field in AdS black holes and the decay rates in the dual field theory. The first study of the scalar quasinormal modes in AdS space was performed by Chan and Mann [3]. For Bañados-Teitelboim-Zanelli (BTZ) black holes, exact expressions for the quasinormal modes were obtained by Cardoso and Lemos for scalar, electromagnetic, and Weyl perturbations [4]. In this context, the connection of CFT and quasinormal modes was explored by Birmingham et al. [5]. The problem in higher dimensions was considered by Horowitz and Hubeny [6]. Their basic results were confirmed in [7] by direct calculation of the wave functions. Some other perturbations in AdS backgrounds were treated in [8]. For asymptotically de Sitter spacetimes, similar conjectures have been formulated. Strominger [9] proposed a holographic duality relating quantum gravity on ddimensional de Sitter space (dSd) to a conformal field the-