Decoupling and non-decoupling dynamics of large D black holes

Self Cite

134

Abstract:We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable GregoryLaflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k 9 for the sound mode and to k 8 for the shear mode.

Section: Introductionmentioning

confidence: 83%

Quasinormal modes of (anti-)de Sitter black holes in the 1/D expansion

Emparan

Suzuki

Tanabe

2015

Self Cite

134

“…for the decoupled perturbations [7] the black hole can be effectively regarded as a thin membrane [11,12] with the thickness ∼ r 0 /D. The shape of the membrane that is the topology of the horizon is described by the embedding of the membrane into a background spacetime, and the non-linear dynamics of the membrane is determined by the effective equations obtained by integrating out the radial direction of the Einstein equations.…”

Section: Jhep04(2017)167mentioning

confidence: 99%

“…This makes the perturbation problems such as the computation of the quasinormal modes (QNMs) [7][8][9][10] much simpler. Moreover…”

Section: Introductionmentioning

confidence: 99%

Charged black rings at large D

Chen¹,

Li²,

Wang³

2017

Abstract:We study the charged slowly rotating black holes in the Einstein-Maxwell theory in the large dimensions (D). By using the 1/D expansion in the near regions of the black holes we obtain the effective equations for the charged slowly rotating black holes. The effective equations capture the dynamics of various stationary solutions, including the charged black ring, the charged slowly rotating Myers-Perry black hole and the charged slowly boosted black string. Via different embeddings we construct these stationary solutions explicitly. For the charged black ring at large D, we find that the charge lowers the angular momentum due to the regularity condition on the solution. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the charge perturbation and the gravitational perturbation analytically. Like the neutral case the charged thin black ring suffers from the Gregory-Laflamme-like instability under the non-axisymmetric perturbations, but the charge weakens the instability. Besides, we find that the large D analysis always respects the cosmic censorship.

“…The essence in the large D expansion is that when the spacetime dimension is sufficiently large D → ∞, the gravitational field of a black hole is strongly localized near its horizon due to the dominant radial gradient of the gravitational potential. As a result, for the decoupled quasinormal modes [5] the black hole can be effectively taken as a surface or membrane embedded in the background spacetime [6][7][8][9][10][11]. The membrane is described by the way it is embedded into the background spacetime, and its nonlinear dynamics is determined by the effective equations obtained by integrating the Einstein equations in the radial direction.…”

Section: Introductionmentioning

confidence: 99%

Static Gauss-Bonnet black holes at large D

Chen¹,

Li²

2017

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.