In the context of AdS/CFT, gravitational shockwaves serve as a geometric manifestation of boundary quantum chaos. We study this connection in general diffeomorphism-invariant theories involving an arbitrary number of bosonic fields. Specifically, we demonstrate that theories containing spin-2 or higher-spin fields generally admit classical localized shockwave solutions on black hole backgrounds, whereas spin-0 and spin-1 theories do not. As in the gravitational case, these higher-spin shockwaves provide a means to compute the out-of-time-order correlator. Both the Lyapunov exponent and the butterfly velocity are found to universally agree with predictions from pole skipping. In particular, higher-spin fields lead to a Lyapunov exponent that violates the chaos bound and a butterfly velocity that may exceed the speed of light.
We study collisions between localized shockwaves inside a black hole interior. We give a holographic boundary description of this process in terms of the overlap of two growing perturbations in a shared quantum circuit. The perturbations grow both exponentially as well as ballistically. Due to a competition between different physical effects, the circuit analysis shows dependence on the transverse locations and exhibits four regimes of qualitatively different behaviors. On the gravity side we study properties of the post-collision geometry, using exact calculations in simple setups and estimat…
We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. The bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice ca…
在膜引力中，我们构造了定域在张膜上的相对论性粒子的精确引力场解。它们是4D de Sitter空间中引力激波的推广。我们提供了正常的分支和自膨胀分支DGP braneworlds的度量，并将它们与4D爱因斯坦引力解进行比较，并与引力只存在于5D块体中而没有任何膜局部曲率项的情况进行比较。在短距离上，波的轮廓看起来与四维中的相同。这些修正只出现在远离源的地方，它们与4D de Sitter空间中的长距离修正不同。我们还发现了一个新的非微扰通道的能量发射到散装从自膨胀的分支，当重力在德西特半径修改。
Gravitational Shock Waves and Their Scattering in Brane-Induced Gravity
本文继hep-th/0501028之后，详细推导和讨论了在膜诱导引力作用下局域于张膜上的相对论性粒子的精确引力场解。我们的推导产生正常分支和自膨胀分支DGP braneworlds的度量。他们推广了德西特空间中的四维引力激波，因此我们将它们与相应的四维广义相对论解以及引力只存在于五维体中且没有膜定域引力子动力学项的情况进行了比较。我们写下来的解决方案，在两个变量的超几何函数，并发现在短距离的冲击波轮廓看起来完全相同的4D闵可夫斯基空间，从而恢复的限制，如果重力是介导的亚稳态，但寿命长，批量共振。远离源的校正不同于4D de Sitter空间中的长距离校正，具有距离的奇次幂。我们详细讨论了自膨胀分支上的极限情况下，当重力被修改正好在德西特半径，能量可以通过共振过程损失到大部分。最后，我们考虑了膜上的普朗克散射，并发现对于足够小的碰撞参量，它非常接近通常的4D描述。
We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by exploiting a novel relation between scattering amplitudes and solutions to Einstein's field equations. We prove that gravitational shock waves arise from the classical part of a three point function with two massless scalars and a graviton. The region where radiation is localized has a distributional profile and it is now recovered in a natural way, thus bypassing t…
