Currents and radiation from the large D black hole membrane

Abstract:We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large number of dimensions satisfy the aforementioned restrictions and their dynamics are captured by hydrodynamics with a naturally truncated derivative expansion. Using analytic and numerical techniques we analyze two and three-dimensional turbulent flow of such fluids in various regimes and its relation to geometric data.

Section: Jhep04(2018)065mentioning

confidence: 99%

Holographic turbulence in a large number of dimensions

Rozali

Sabag

Yarom

2018

“…If the rotation is still as small as the one in the Einstein theory, then the construction of the corresponding black ring solution might be feasible. It would be interesting to study the radiation of the black ring solution in the framework of the membrane paradigm as well [47].…”

Section: Jhep04(2017)167mentioning

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.

“…We wish the large D analysis may shed light on this interesting issue. Moreover, it is certainly interesting to address various issues of the Gauss-Bonnet black holes in the framework of membrane paradigm developed in [34][35][36][37][38].…”

Section: Jhep05(2017)025mentioning

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.