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arXiv 0712.2289hep-thgr-qc
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视界附近的非平衡态热力学与全息

Non-equilibrium thermodynamics near the horizon and holography

Mitsutoshi Fujita

摘要:

在AdS/CFT对应的对偶理论中,黑膜的小扰动被解释为与热力学平衡的小偏差。本文采用膜范式计算了对偶杨-米尔斯理论在重力场的流体力学性质。这种方法不同于通常的AdS/CFT对应,它不是在边界上而是在离视界稍远的地方计算经典解。重力扰动有声模和剪切模。对于健全的模式,这样的计算在地平线上还没有完成。然后,我们发现视界处的边界应力张量满足平坦空间中的守恒定律,并且可以用全息术表示对偶理论中应力张量的耗散部分。利用它们,我们可以直接读出对偶理论的剪切粘度和体积粘度。准正规模是线性化方程的解,它服从于特定边界条件下引力背景的经典涨落,也是规范不变的量。我们使用的解决方案,组成这样的数量,每个波动,并表明准正规模式是一致的膜范例。

英文摘要:

Small perturbations of a black brane are interpreted as small deviations from thermodynamic equilibrium in a dual theory with the AdS/CFT correspondence. In this paper, we calculate hydrodynamics of the dual Yang-Mills theory in the gravity side using membrane paradigm. This method is different from the usual AdS/CFT correspondence and evaluate classical solutions not at boundaries but at the place slightly away from a horizon. There are sound modes or shear modes for gravity perturbation. For sound modes, such calculation at the horizon has not yet been done. Then, we find that boundary stress tensor at the horizon satisfies conservation law in flat space and can represent dissipative parts of stress tensor in the dual theory by holography. Using them, we can read off directly shear and bulk viscosity of the dual theory. Quasinormal modes are solutions to linearized equations obeyed by classical fluctuations of a gravitational background subject to specific boundary conditions and are also gauge-invariant quantities. We use solutions for each fluctuation that compose such quantities and show that quasinormal modes are consistent with the membrane paradigm.

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