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

对称性在物理学和天文学中起着至关重要的作用。它们通常与守恒量有关，这些守恒量允许对物理系统有更清晰的了解。该奖项支持的研究特别感兴趣的是黑洞地平线上存在的对称性。这对引力散射实验、引力记忆测量、旋转黑洞的天文测量和量子黑洞信息都有潜在的影响。这个项目的目标是进一步研究这些对称性以及它们在物理系统中所起的作用。在过去的几年里，Strominger和他的团队已经证明，在类光无限大处的无限多个对称构成了三个现象的精确三角等价的一部分，这三个现象普遍存在于各种物理系统中，半个世纪以来已经被分别研究--另外两个现象是记忆和软定理。软定理描述了物理系统的低能量行为，并且可以作为无限多个对称的‘Ward恒等式’来推导。第三个角--记忆--被证明是软定理的傅里叶变换。这种非常简单的三角等价在物理学中的各种情况下都会发生：QED、杨-米尔斯理论、重力，在任何维度，无论是否具有超对称性，在一个角落里都有领先、次要或次要的软定理。虽然已经填写了几个三角形，但大多数仍未完成。三角形的每个实例都有自己的特殊和迷人的特征，这将在本项目中进行研究。最近，三角形结构被发现对著名的黑洞信息之谜有着深远的影响，这一谜题也将被追查。在另一个方向上，广义相对论意味着极端克尔近视界区域的动力学受无限维涌现共形对称性的支配。精密黑洞光谱学现在已经发展到天文学家开始观察受这种共形对称性支配的时空区域的阶段。该奖项将支持对共形对称性潜在观测后果的系统探索。

Symmetries play a critical role in physics and astronomy. They are usually associated with conserved quantities that allow for a clearer picture of a physical system. Of particular interest to the research supported by this award are symmetries present at the horizon of black holes. These have potential implications for gravitational scattering experiments, gravitational memory measurements, astronomical measurements of spinning black holes and quantum black hole information. The objective of this project is to further investigate these symmetries and the role that they play in physical systems. In the last few years, Strominger and group have shown that the infinitely many symmetries at light-like infinity form one part of an exact triangular equivalence of three phenomena which recur ubiquitously across a wide variety of physical systems and have been separately studied for a half century -- the other two phenomena being memory and soft theorems. Soft theorems characterize the low energy behavior of physical systems and can be derived as the `Ward identities' of the infinite number of symmetries. The third corner -- memory -- turns out to be simply the Fourier transform of the soft theorems. This very simple triangular equivalence occurs in various instances in physics: QED, Yang-Mills theory, gravity, in any number of dimensions, with or without supersymmetry, with leading, subleading or subsubleading soft theorems in one corner. While several triangles have been filled out, most remain incomplete. Each instance of the triangle has its own special and fascinating features, which will be investigated in this project. More recently, the triangular structure was found to have profound implications for the famous black hole information puzzle, which will also be pursued. In another direction, general relativity implies that the dynamics of the near horizon region of extreme Kerr is governed by an infinite-dimensional emergent conformal symmetry. Precision black hole spectroscopy has now advanced to the stage where astronomers are beginning to observe the regions of spacetime governed by this conformal symmetry. This award will support a systematic exploration of potential observational consequences of the conformal symmetry.