Linear stability of Einstein-Gauss-Bonnet static spacetimes: Tensor perturbations

Dotti, Gustavo; Gleiser, Reinaldo J.

doi:10.1103/physrevd.72.044018

Cited by 131 publications

(159 citation statements)

References 34 publications

Supporting

Mentioning

151

Contrasting

Unclassified

Order By: Relevance

“…It is intrinsically related to the breakdown of the well-posedness of the initial value problem [17]. A similar instability was found for asymptotically flat [18][19][20] and de Sitter black holes [21] in Gauss-Bonnet theories, as well as for planar EinsteinLovelock [22], spherical pure Lovelock (i.e. without the Einstein term) black holes [23], and for small charged Lovelock black holes [24,25].…”

Section: Jhep09(2017)139mentioning

confidence: 73%

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Konoplya

Zhidenko

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

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.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:2 ))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 λ GB ) 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 |λ GB | > 1/8 and has anomalously large relaxation time when approaching the threshold of instability.

show abstract

Section: Jhep09(2017)139mentioning

confidence: 73%

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Konoplya

Zhidenko

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…It has been investigated for the Gauss-Bonnet black holes since their findings. For the asymptotically flat Gauss-Bonnet black holes it was found in [21,22] that such black holes are unstable against gravitational perturbations in five and six dimensions but become stable in higher dimensions [23]. For a Gauss-Bonnet black hole with a positive cosmological constant, it was shown in [24] that the black holes becomes unstable in D ≥ 5 dimensions at sufficiently large values of the cosmological constant.…”

Section: Jhep05(2017)025mentioning

confidence: 99%

Static Gauss-Bonnet black holes at large D

Chen¹,

Li²

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the static black holes in the large D dimensions in the Gauss-Bonnet gravity with a cosmological constant, coupled to the Maxewell theory. After integrating the equation of motion with respect to the radial direction, we obtain the effective equations at large D to describe the nonlinear dynamical deformations of the black holes. From the perturbation analysis on the effective equations, we get the analytic expressions of the frequencies for the quasinormal modes of charge and scalar-type perturbations. We show that for a positive Gauss-Bonnet term, the black hole could become unstable only if the cosmological constant is positive, otherwise the black hole is always stable. However, for a negative Gauss-Bonnet term, we find that the black hole could always be unstable. The instability of the black hole depends not only on the cosmological constant and the charge, but also significantly on the Gauss-Bonnet term. Moreover, at the onset of instability there is a non-trivial static zero-mode perturbation, which suggests the existence of a new nonspherically symmetric solution branch. We construct the non-spherical symmetric static solutions of the large D effective equations explicitly.

show abstract

“…For such a restricted class of Lovelock theory-though most generic in D = 5, 6, the master equations for metric perturbations have previously been derived by Dotti and Gleiser. 41), 42) A numerical analysis of the (in)stability of static black holes in Einstein-Gauss-Bonnet theory in dimensions D = 5, ..., 11 has been performed in Ref. 45).…”

Section: Lovelock Black Holesmentioning

confidence: 99%

Chapter 6. Perturbations and Stability of Static Black Holes in Higher Dimensions

Ishibashi

Kodama

2011

Prog. Theor. Phys. Suppl.

146

View full text Add to dashboard Cite

In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case. We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of (m+n)-dimensional spacetimes with a warped product metric, including black hole geometry. We classify perturbations of such a background into three types, the tensor, vector and scalar-type, according to their tensorial behavior on the n-dimensional part of the background spacetime, and for each type of perturbations, we introduce a set of manifestly gauge invariant variables. We then introduce harmonic tensors and write down the equations of motion for the expansion coefficients of the gauge invariant perturbation variables in terms of the harmonics. In particular, for the tensor-type perturbations a single master equation is obtained in the (m + n)-dimensional background, which is applicable for perturbation analysis of not only static black holes but also some class of rotating black holes as well as black-branes. For the vector and scalar type, we derive a set of decoupled master equations when the background is a (2 + n)-dimensional static black hole in the Einstein-Maxwell theory with a cosmological constant. As an application of the master equations, we review the stability analysis of higher dimensional charged static black holes with a cosmological constant. We also briefly review the recent results of a generalization of the perturbation formulae presented here and stability analysis to static black holes in generic Lovelock theory.

show abstract

Linear stability of Einstein-Gauss-Bonnet static spacetimes: Tensor perturbations

Cited by 131 publications

References 34 publications

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Static Gauss-Bonnet black holes at large D

Chapter 6. Perturbations and Stability of Static Black Holes in Higher Dimensions

Contact Info

Product

Resources

About