Topics In General Relativity

广义相对论主题

• 批准号: 2207659
• 负责人: Andrew Strominger
• 金额: $ 40.39万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-15 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2207659&HistoricalAwards=false
• 关键词: Topics; General; Relativity

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.

PI的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。最重要的目标是找到一种用量子力学来描述引力的方法：一个多世纪以来，这两个领域一直无法统一。这里所描述的项目是建立在最近对粒子理论家研究软定理和相对主义者研究时空渐近边界的长期建立的技术的综合之上的。这种综合激发了不同领域物理学家之间丰富的合作，从扭曲理论到LIGO再到弦理论。它既带来了新的实验预测（关于新的记忆效应），也带来了对时空的新的具体见解，就像纽曼和彭罗斯很久以前预言的天球量子理论一样，最近又转世为全息原理。这项事业是由一群不同寻常的年轻理论物理学家推动的。施特罗明格和合作者将继续研究爱因斯坦方程所隐含的无限多非平凡作用的精确对称性。它们出现在深红外线中，既存在于零无穷远的渐近平坦时空中——在那里它们被美丽而有力地重塑为天球的对称性——也存在于黑洞视界附近。这一理论研究对引力散射、引力记忆、即将到来的事件视界望远镜（EHT）观测和黑洞信息悖论具有潜在的意义。他们将进一步发展三种无处不在的现象：记忆、软定理和渐近对称的强大而精确的三角等价。量子场论中的软定理涉及有或没有“软”（低能）粒子（如引力子）插入的多粒子散射过程。渐近对称（如BMS）是在无穷远处对物理数据起非平凡作用的微分同态。软定理可以导出为与渐近对称相关的守恒定律的量子矩阵元素，并且是引力记忆效应公式的傅里叶变换。本研究计划将发展重力和规范理论中三角等价的许多重复实例。他们打算回答如何在四个渐近平坦的时空维度中列举广义相对论的所有非平凡渐近对称性的中心问题。在过去的授权周期中，研究表明，引力散射振幅可以在零无穷远的天球上被重塑为共形相关，在那里，二维共形场论的强大工具可以被利用，从而在未来实现对非平凡渐近对称性的完整理解。最近，物理上可观察到的对称性被组织成一个称为w（1+∞）的群体，这是一个重要的步骤，为扭转理论提供了直接的联系。将三角形结构应用于黑洞，意味着黑洞远不是没有特征的物体，即使是经典的黑洞也有无限的“软头发”。这一发现为黑洞信息悖论带来了新的研究思路。各种克尔黑洞对称性的观测特征将被研究。广义相对论暗示极端克尔黑洞的近视界区域的动力学和任何克尔黑洞光子环附近的光线都显示保形尺度对称。精密黑洞成像技术的进步使天文学家能够观测到受这些对称性支配的时空区域，该项目将探索它们潜在的观测结果。该奖项反映了美国国家科学基金会的法定使命，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。