We discuss the derivation of dissipative Bjorken hydrodynamics from a Schwarzschild black hole in asymptotically AdS spacetime of arbitrary dimension in the limit of large longitudinal proper time $τ$. Using an appropriate slicing near the boundary, we calculate the Schwarzschild metric to next-to-next-to-leading order in the large $τ$ expansion as well as the dual stress-energy tensor on the boundary via holographic renormalization. At next-to-next-to-leading order, it is necessary to perturb the Schwarzschild metric in order to maintain boost invariance. The perturbation has a power law time dependence and leads to the same value of the ratio of viscosity to entropy density, $1/(4π)$, as in the case of sinusoidal perturbations. Our results are in agreement with known time-dependent asymptotic solutions of the Einstein equations in five dimensions.
We consider a large black hole in asymptotically AdS spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions.
I discuss two examples of time-dependent flow which can be described in terms of an AdS Schwarzschild black hole via holography. The first example involves Bjorken hydrodynamics which should be applicable to the formation of the quark gluon plasma in heavy ion collisions. The second example is the cosmological evolution of our Universe.
Extending the quantum effective approach of Son and Nicolis and incorporating dissipation, we develop a MIS formalism for describing a superfluid out of equilibrium by including the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We find that the evolution of the superfluid undergoing Bjorken flow is governed by the conventional hydrodynamic attractor with unbroken symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponenti…
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；National Centre for Nuclear Research（国家核研究中心）；University of Białystok（比亚韦斯托克大学）
We found that the Wigner rotation of a particle with spin 1/2, which is unitary in Minkowski spacetime, becomes non-unitary as the particle is falling onto the black hole. This implies that, from the quantum information processing point of view, any quantum information encoded in spins will be dissipated near the black hole. The gravitational field around the black hole thus acts like a dissipative quantum channel, especially the bit flip channel.
We analyse the global structure of time-dependent geometries dual to expanding plasmas, considering two examples: the boost invariant Bjorken flow, and the conformal soliton flow. While the geometry dual to the Bjorken flow is constructed in a perturbation expansion at late proper time, the conformal soliton flow has an exact dual (which corresponds to a Poincare patch of Schwarzschild-AdS). In particular, we discuss the position and area of event and apparent horizons in the two geometries. The conformal soliton geometry offers a sharp distinction between event and apparent horizon; whereas t…
We study the AdS/CFT thermodynamics of the spatially isotropic counterpart of the Bjorken similarity flow in d-dimensional Minkowski space with d>=3, and of its generalisation to linearly expanding d-dimensional Friedmann-Robertson-Walker cosmologies with arbitrary values of the spatial curvature parameter k. The bulk solution is a nonstatic foliation of the generalised Schwarzschild-AdS black hole with a horizon of constant curvature k. The boundary matter is an expanding perfect fluid that satisfies the first law of thermodynamics for all values of the temperature and the spatial curvature, …
We consider a gravity dual description of time dependent, strongly interacting large-Nc N=4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that is relevant to RHIC experiments. We obtain the dual geometry at the late time that is consistent with dissipative hydrodynamics. We show that the integration constants that cannot be determined by hydrodynamics are given by looking at the horizon of the dual geometry. Relationship between time dependence of the energy density and bulk singularity is also di…
We derive a long wavelength effective point particle description of four-dimensional Schwarzschild black holes. In this effective theory, absorptive effects are incorporated by introducing degrees of freedom localized on the worldline that mimic the interaction between the horizon and bulk fields. The correlation functions of composite operators in this worldline theory can be obtained by standard matching calculations. For example, we obtain the low frequency two-point function of multipole worldline operators by relating them to the long wavelength graviton black hole absorptive cross sectio…
One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background. We also consider as a concrete example linearized metric perturbations of a five-dimensional…
Indian Association for the Cultivation of Science（印度科学培养协会）；Sapienza Università di Roma（罗马第一大学）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；University of Chinese Academy of Sciences（中国科学院大学）
