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

Harvard University, Cambridge MA

Investigators

Abstract

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.