Quasinormal spectrum and the black hole membrane paradigm
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 670:4-5 (2009) 442-445
Abstract:
The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (black brane) in terms of the background metric components. The resulting dispersion relation is identical to the one obtained in the membrane paradigm treatment of the diffusion on stretched horizons. Combined with the Buchel-Liu universality theorem for the membrane's diffusion coefficient, our result means that in the long wavelength limit the black brane spectrum of gravitational perturbations exhibits a universal, purely imaginary quasinormal frequency. In the context of gauge-gravity duality, this provides yet another (third) proof of the universality of shear viscosity to entropy density ratio in theories with gravity duals. © 2008 Elsevier B.V. All rights reserved.Holographic Quantum Liquid
PHYSICAL REVIEW LETTERS 102:5 (2009) ARTN 051602
Relativistic viscous hydrodynamics, conformal invariance, and holography
Journal of High Energy Physics 2008:4 (2008)
Abstract:
We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled = 4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Müller-Israel- Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.Viscosity, black holes, and quantum field theory
Annual Review of Nuclear and Particle Science 57 (2007) 95-118
Abstract:
We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasi-normal modes of the AdS black p-brane metric. We provide proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned. Copyright © 2007 by Annual Reviews. All rights reserved.Holographic spectral functions and diffusion constants for fundamental matter
Journal of High Energy Physics 2007:11 (2007)