Chaos and pole-skipping in rotating black holes
Chaos and pole-skipping in rotating black holes
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DOI：
10.1007/jhep01(2022)013
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发表时间：
2021-11
影响因子：
5.4
通讯作者：
Mike Blake;R. Davison
中科院分区：
文献类型：
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作者：
Mike Blake;R. Davison
我们研究了 Kerr-AdS 黑洞对偶全息理论的多体量子混沌与能量动力学之间的联系。特别是，我们确定了一个控制引力冲击波角剖面的偏微分方程，该偏微分方程与超时有序相关函数（OTOC）的计算相关。我们进一步表明，这种冲击波轮廓与边界理论中的能量涨落行为直接相关。特别是，我们使用 Teukolsky 形式证明，在复数频率 ω*= i2πT 下，只要地平线附近的度量扰动的角度轮廓满足该冲击波方程，线性化爱因斯坦方程就存在一个额外的输入解。因此，对于具有这种时间和角度轮廓的度量扰动，我们发现边界理论的能量密度响应表现出“跳极”的特征——即，它是未定义的，但在轮廓的参数小变形上表现出集体模式。此外，我们还对缓慢旋转的大黑洞在赤道平面上的 OTOC 进行了显式计算，并表明其形式可用于获得对偶 CFT 中集体模式色散关系的约束。
We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency ω∗= i2πT there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of “pole-skipping”—namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT.