全息热化、AdS的稳定性和费米-帕斯塔-乌拉姆-钦古佯谬
Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
摘要：
对于具有负宇宙学常数的广义相对论中的实无质量标量场，我们揭示了一大类接近AdS的球对称初始条件，但其数值演化不会导致黑洞的形成.根据AdS/CFT字典，这些批量解决方案是对偶状态的强相互作用的边界CFT，未能热化在晚些时候。此外，由于这些状态不是静止的，它们定义了不平衡的动态CFT配置。我们开发了一个两个时间尺度的微扰形式主义，捕捉直接和逆级联的能量，并同意我们完全非线性演化在适当的制度。我们还表明，这种形式主义承认一个大类的拟周期解。最后，我们证明了一个惊人的平行动态AdS和经典的费米-Pasta-Ulam-Tsingou问题。
英文摘要：
For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to AdS, but whose numerical evolution does not result in black hole formation. According to the AdS/CFT dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-timescale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasi-periodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.
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