Topics In General Relativity

圆周率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，这两个领域一直在抵制统一。这里描述的项目建立在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确立的技术的最新综合的基础上。这一综合点燃了不同领域的物理学家之间的富有成效的合作，从扭曲理论到LIGO再到弦理论。这既导致了新的实验预测(对新的记忆效应)，也导致了对时空的新的具体见解，时空是关于天球的量子理论，很久以前纽曼和彭罗斯预先假设了这一点，最近转世为全息原理。斯特罗明格和他的合作者将继续研究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。它们出现在深红外中，既出现在零无限大的渐近平坦的时空中-在那里它们被美丽而有力地重塑为天球的对称性-也出现在黑洞的地平线附近。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都有潜在的影响。它们将进一步发展三种普遍现象的强大而精确的三角等价：记忆、软定理和渐近对称。量子场论中的软定理涉及多粒子的散射过程，包括插入和不插入“软”(低能)粒子，如引力子。渐近对称(如BMS)是作用于无穷远处的物理数据的非平凡的微分同胚。软定理可以被导出为与渐近对称相关的守恒律的量子矩阵元素，并且是引力记忆效应公式的傅里叶变换。这项研究计划将在引力和规范理论中发展这种三角等价的许多反复出现的例子。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度中列举广义相对论的所有非平凡渐近对称。在过去的资助周期中，研究表明，引力散射振幅可以被重塑为零无限天球上的共形相关器，在那里可以利用二维共形场论的强大工具，使人们对未来可以到达的非平凡渐近对称性有一个完整的理解。就在最近，物理上可观察到的对称性被组织成称为w(1+无穷大)的群，这是提供与扭曲理论直接联系的重要一步。应用到黑洞上，这种三角形结构意味着，即使是经典的黑洞，也远不是光秃秃的无特征物体，而是有着无穷无尽的“柔软头发”。这种洞察力导致了对黑洞信息悖论的新的探究。我们将研究各种克尔黑洞对称性的观测特征。广义相对论表明，任何克尔黑洞的极克尔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具有共形标度对称性。精密黑洞成像的进步开始允许天文学家观察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。这一奖项反映了美国国家科学基金会的法定任务，并通过使用基金会的智力优势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.