Topics In General Relativity

PI小组将在我们对爱因斯坦广义相对论的经典和量子方面的理解的边界上向前推进。首要目标是找到一种方法来描述引力在量子力学方面：两个领域已经抵制统一超过世纪。这里描述的项目建立在最近的综合长期建立的技术，在软定理的粒子理论家和相对论的时空渐近边界的研究中开发。这种综合激发了从扭量理论到LIGO再到弦理论等不同领域的物理学家之间的丰富合作。它导致了新的实验预测（关于新的记忆效应）和新的具体见解，即时空作为天球上的量子理论，这是纽曼和彭罗斯很久以前就有先见之明地假设的，最近又化身为全息原理。这项事业是由一群异常多样化和年轻的理论物理学家推动的。斯特罗明格和合作者将继续他们对爱因斯坦方程所隐含的无限多个非平凡作用的精确对称性的研究。它们出现在深红外线中，既出现在零无穷远处的渐近平坦时空中--在那里它们被美丽而有力地重塑为天球的对称性--也出现在黑洞的视界附近。这项理论研究对引力散射、引力记忆、事件视界望远镜（EHT）即将进行的观测以及黑洞信息悖论具有潜在的意义。他们将进一步发展三种普遍存在的现象的强大和精确的三角等价：记忆，软定理和渐近对称。量子场论中的软定理涉及多粒子散射过程中有和没有“软”（低能）粒子的插入，如引力子。渐近对称（如BMS）是一种非平凡地作用于无穷远处的物理数据的同构。软定理可以作为与渐近对称性相关的守恒律的量子矩阵元导出，并且是引力记忆效应公式的傅里叶变换。这个研究计划将发展在引力和规范理论中三角等价的许多重复的例子。他们打算回答一个中心问题，即如何在四个渐近平坦的时空维中枚举广义相对论的所有非平凡渐近对称性。在过去的资助周期中，人们发现引力散射振幅可以在零无穷远处的天球上被重新塑造为共形的散射子，在那里可以利用二维共形场论的强大工具，从而在未来实现对非平凡渐近对称性的全面理解。最近，物理上可观察到的对称性组成了w（1+无穷大）群，这是与扭量理论直接联系的重要一步。应用到黑洞，三角形结构意味着，即使是经典的黑洞，也远不是光秃秃的无特征的物体，而是携带着无限的“柔软的头发”。这一发现为黑洞信息悖论的研究开辟了新的思路。各种克尔黑洞对称性的观测签名将被调查。广义相对论意味着极端Kerr黑洞的近视界区和任何Kerr黑洞光子环附近的光线都具有共形标度对称性。在精确的黑洞成像方面的进展开始使天文学家能够观测由这些对称性支配的时空区域，该项目将探索其潜在的观测结果。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The PI's group will push forward at the boundaries of our understanding of both classical and quantum aspects of Einstein's theory of general relativity. The overarching goal is to find a way to describe the gravitational force in terms of quantum mechanics: two fields that have resisted unification for more than a century. The projects described here build on a recent synthesis of long-established techniques developed in the study of soft theorems by particle theorists and in the study by relativists of the asymptotic boundaries of spacetime. This synthesis has ignited a fertile collaboration between physicists in disparate fields from twistor theory to LIGO to string theory. It has led to both new experimental predictions (of novel memory effects) and new concrete insights into spacetime as a quantum theory on the celestial sphere as presciently hypothesized long ago by Newman and Penrose and recently reincarnated as the holographic principle. This enterprise in being driven by an unusually diverse and young group of theoretical physicists.Strominger and collaborators will continue their investigation of the infinitely many nontrivially- acting exact symmetries implied by the Einstein equations. These arise in the deep infrared, both in asymptotically flat spacetimes at null infinity – where they are beautifully and powerfully recast as symmetries of the celestial sphere – and near the horizon of a black hole. This theoretical research has potential implications for gravitational scattering, gravitational memory, upcoming observations at the Event Horizon Telescope (EHT), and the black hole information paradox. They will further develop the powerful and exact triangular equivalence of three ubiquitous phenomena: memory, soft theorems, and asymptotic symmetries. Soft theorems in quantum field theory relate multi-particle scattering process with and without insertions of “soft” (low-energy) particles, such as gravitons. Asymptotic symmetries (such as BMS) are diffeomorphisms that act nontrivially on the physical data at infinity. Soft theorems can be derived as quantum matrix elements of conservation laws associated to the asymptotic symmetries, and are the Fourier transform of the formula for the gravitational memory effect. This research program will develop the many recurring instances of this triangular equivalence in both gravity and gauge theory. They intend to answer the central question of how to enumerate all the non- trivial asymptotic symmetries of general relativity in four asymptotically flat spacetime dimensions. In the past grant cycle, it was shown that gravitational scattering amplitudes can be recast as conformal correlators on the celestial sphere at null infinity, where the powerful tools of two-dimensional conformal field theory can be exploited, bringing a complete understanding of the nontrivial asymptotic symmetries within future reach. Very recently it was that physically observable symmetries organize into the group known as w(1+infinity), a significant step that provides direct connections to twistor theory. Applied to black holes, the triangular structure implies that, far from being bald featureless objects, even classical black holes carry an infinite head of “soft hair.” This insight has led to new lines of inquiry into the black hole information paradox. Observational signatures of various Kerr black hole symmetries will be investigated. General relativity implies that the dynamics of the near-horizon region of extreme Kerr and light rays near the photon ring of any Kerr black hole both display conformal scaling symmetries. Advances in precision black hole imaging are beginning to allow astronomers to observe the regions of spacetime governed by these symmetries, and the project will explore their potential observational consequences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.