Abstract
Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling α. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in α correction to the damping rates: ω≈ReωSAdS −ImωSAdS(1−α·((D+1)(D−4)/2R2))i, where R is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when α goes to zero. When the black hole radius is much larger than the anti-de Sitter radius R, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling α (or used in holography λGB) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, D = 5 black brane is unstable at |λGB| > 1/8 and has anomalously large relaxation time when approaching the threshold of instability.
Highlights
The above results were obtained at the assumption that the dual field theory has large ‘t Hooft coupling λ [7]
Here we shall show that there is no other instability for the EinsteinGauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail
If the Gauss-Bonnet coupling α is not small enough, the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity
Summary
The Lagrangian of the D-dimensional Einstein-Gauss-Bonnet theory has the form: L. Let us describe the range of parameters corresponding to such a black hole with the required AdS asymptotic at a negative Λ-term. As we shall have to investigate the spacetime behavior outside the black hole only, it is useful to express the black hole mass in terms of its size by introducing the radius of the event horizon rH > 0. Other basic properties of Einstein-Gauss-Bonnet-AdS black holes were considered in [37]. Holographic community analyzes mostly black holes with planar horizons and, following the hydrodynamic analogies, calls the corresponding channels: sound, shear and scalar (see table 1). The Gauss-Bonnet coupling λGB used usually in holography, and the coupling α used in gravity are related as follows: 2Λα α. One can check that, in this limit formulas (44), (51), and (53) of [31], obtained for black holes, coincide, respectively, with (2.79), (2.80), and (2.81) of [14] for black branes
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