Abstract
Holography relates the quasinormal modes frequencies of AdS black holes to the pole structure of the dual field theory propagator. These modes thus provide the timescale for the approach to thermal equilibrium in the CFT. Here, we study how such pole structure and, in particular, the time to equilibrium can get modified in the presence of a black hole hair. More precisely, we consider in AdS a set of relaxed boundary conditions that allow for a low decaying graviton mode near the boundary, which triggers an additional degree of freedom. We solve the scalar field response on such background analytically and non-perturbatively in the hair parameter, and we obtain how the pole structure gets affected by the presence of a black hole hair, relative to that of the usual AdS black hole geometry. The setup we consider is a massive 3D gravity theory, which admits a one-parameter family deformation of BTZ solution and enables us to solve the problem analytically. The theory also admits an AdS$_3$ soliton which gives a family of vacua that can be constructed from the hairy black hole by means of a double Wick rotation. The spectrum of normal modes on the latter geometry can also be solved analytically; we study its properties in relation to those of the AdS$_3$ vacuum.
Highlights
Three-dimensional gravity [1] has proven to be a fruitful arena to investigate different aspects of the AdS=CFT correspondence [2] that, in other setups, could hardly be addressed
We solve the scalar field response on such background analytically and nonperturbatively in the hair parameter, and we obtain how the pole structure gets affected by the presence of a black hole hair, relative to that of the usual AdS black hole geometry
Quasinormal modes provide the timescale for the approach to thermal equilibrium. This means that the quantization conditions coming from the quasinormal modes (QNM) computation in the AdS3 black hole geometry are in correspondence with the pole structure of the propagator in the dual CFT2 at finite temperature
Summary
Three-dimensional gravity [1] has proven to be a fruitful arena to investigate different aspects of the AdS=CFT correspondence [2] that, in other setups, could hardly be addressed. Some features of these different CFTs may be shared among them, as they may be associated to particular aspects of the bulk theory that are indistinguishable This enables one to speculate about the possibility of finding a consistent geometric dual description for a broader class of CFTs. In this paper, we will study the so-called new massive gravity (NMG) [18], which is a parity-even theory of 3D gravity that has very interesting properties. Quasinormal modes provide the timescale for the approach to thermal equilibrium This means that the quantization conditions coming from the QNM computation in the AdS3 black hole geometry are in correspondence with the pole structure of the propagator in the dual CFT2 at finite temperature.
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