Classical and Quantum Aspects of Black Holes, Horizons and Asymptotic Symmetries

斯特罗明格和他的合作者将研究爱因斯坦引力场方程所隐含的自然界的无限多个对称性，这些对称性是在上一个授予周期中发现的。它们出现在时空的边界上，既有无限大的光状距离，也有快速旋转的黑洞的地平线附近。理论研究在引力波、引力记忆、事件视界望远镜即将进行的天文观测等方面具有潜在的应用价值。Event Horizon望远镜是一项利用位于全球各地的无线电天线阵列来观测黑洞的倡议。该奖项支持的工作还将解决霍金-S黑洞信息悖论，该悖论假设信息可能在黑洞中不被保存。在过去的几年里，这个小组发现了三种现象的精确三角等价，这三种现象普遍存在于各种物理系统中，并已被单独研究了半个多世纪：记忆、软定理和渐近对称。量子场论中的软定理将任何多粒子的散射过程与在没有软粒子的情况下插入引力子这样的“软”(即低能量)粒子到相同的过程相联系。渐近对称(如BMS)是作用于无穷远的物理数据的非平凡的微分同胚。软定理可以作为与渐近对称相关的守恒律的量子矩阵元素来推导。因此，它们具有相同的物理内容。三角形的第三个角是闭合的，注意到引力记忆效应的布拉金斯基-索恩公式正是温伯格软引力子定理在时间上的傅里叶变换。这种三角形有很多反复出现的例子：在量子电动力学中，杨-米尔斯理论，重力，在任何维度，有或没有超对称性，在一个角上有领先的、次要的或次次要的软定理，以及涉及反常的量子三角形。这种对先前已知现象的等价性的发现使我们能够发现全新的现象。给定三角形的一个角，我们现在知道如何找到另外两个角。这个项目研究的是引力三角形。应用于黑洞，这种三角形结构被证明意味着，即使是经典的黑洞，也远不是光秃秃的平凡物体，而是有着无穷无尽的“柔软头发”。霍金1975年关于信息损失的论点假定没有任何这样的显著特征，因此这一论点是无效的。这一洞察力表明，该小组将寻求对黑洞信息悖论进行新的调查。在另一个方向上，天文观测表明，近乎极端的克尔黑洞的存在，其视界以接近光速的速度旋转。广义相对论意味着，极端克尔的高红移、近视界区域，包括最内稳定的圆轨道(ISCO)，其动力学受无限维涌现共形对称性的支配。一般说来，物理系统的对称性既可以有效地表征观测数据，也可以对观测数据产生显著的影响。精密黑洞光谱学已经发展到天文学家开始用各种巧妙的方法观察这种共形对称性所支配的时空区域的阶段。拟议的项目将对共形对称的潜在观测后果进行系统探索，特别是对已经处于数据收集早期阶段的Event Horizon望远镜。

Strominger and collaborators will investigate the infinitely many symmetries of nature implied by the Einstein equations for the gravitational field and discovered under the last grant cycle. These arise at the boundaries of spacetime, both at infinite light like distances and near the horizon of a rapidly spinning black hole. The theoretical research has potential applications to gravitational waves, gravitational memory, upcoming astronomical observations at the Event Horizon telescope. The Event Horizon telescope is an initiative to create observations of black holes of unparalleled resolution using an array of radio antennas located across the globe. The work supported by this award will also tackle Hawking?s black hole information paradox, which posits that information may not be conserved in a black hole. In the last few years, this group has discovered an exact triangular equivalence of three phenomena which recur ubiquitously across a wide variety of physical systems and have been separately studied for over a half century: memory, soft theorems, and asymptotic symmetries. Soft theorems in quantum field theory relate any multi-particle scattering process with the insertion of a 'soft' (i.e. low-energy) particle such as a graviton to the same process without the soft particle.Asymptotic symmetries (such as BMS) are diffeomorphisms which act nontrivially on the physical data at infinity. The soft theorems can be derived as the quantum matrix elements of the conservation laws associated to the asymptotic symmetries. Hence they have the same physical content. The third corner of the triangle is closed by noting that The Braginsky-Thorne formula for the gravitational memory effect is precisely the Fourier transform in time of the Weinberg soft graviton theorem. There are many recurring instances of the triangle: in QED, Yang-Mills theory, gravity, in any number of dimensions, with or without supersymmetry, with leading, subleading or subsubleading soft theorems in one corner, and quantum triangles involving anomalies. This discovery of the equivalence of previously well-understood phenomena enables us to discover brand new phenomena. Given one corner of the triangle, we now know how to find the other two. This project investigates gravitational triangles. Applied to black holes, the triangular structure was shown to imply that, far from being bald featureless objects, even classical black holes carry an infinite head of 'soft hair'. The absence of any such distinguishing features was presumed in Hawking's 1975 argument for information loss, which is therefore invalidated. This insight suggests new lines of investigation into the black hole information paradox which the group will pursue. In another direction, astronomical observation suggests the existence of near-extreme Kerr black holes whose horizons spin at nearly the speed of light. General relativity implies that the dynamics of the high-redshift, near-horizon region of extreme Kerr, which includes the innermost stable circular orbit (ISCO), is governed by an infinite-dimensional emergent conformal symmetry. Symmetries of physical systems in general may both usefully characterize and have striking consequences for observational data. Precision black hole spectroscopy has advanced to the stage where astronomers are beginning to observe -- with a variety of ingenious methods -- the regions of spacetime governed by this conformal symmetry. The proposed project will undertake a systematic exploration of potential observational consequences of the conformal symmetry, in particular for the Event Horizon telescope which is already in the early stages of data collection.