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。它们通常与守恒量相关联，以便更清楚地了解物理系统。该奖项支持的研究特别感兴趣的是黑洞视界的对称性。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意义。这个项目的目标是进一步研究这些对称性及其在物理系统中的作用。在过去的几年里，斯特罗明格和他的团队已经证明，类光无限远处的无限多个对称性形成了三种现象的精确三角等价的一部分，这三种现象在各种物理系统中无处不在，并且已经被单独研究了半个世纪--另外两种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，可以作为无穷多个对称的“沃德恒等式”导出。第三个角--记忆--原来只是软定理的傅立叶变换。这个非常简单的三角等价出现在物理学的各种实例中：QED，杨-米尔斯理论，引力，在任何数量的维度上，有或没有超对称性，在一个角落里有领先，次级或次级软定理。虽然有几个三角形已被填充，但大多数仍不完整。三角形的每一个实例都有其独特而迷人的特征，这将在本项目中进行研究。最近，三角结构被发现对著名的黑洞信息之谜有着深远的影响，这也是我们将要追求的。在另一个方向上，广义相对论意味着极端克尔的近视界区域的动力学是由无限维涌现共形对称决定的。精确的黑洞光谱学现在已经发展到天文学家开始观察由这种共形对称性控制的时空区域的阶段。该奖项将支持系统地探索共形对称性的潜在观测结果。

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.