Aspects of Symmetry in Classical and Quantum Gravity

Abstract

In this thesis, we use symmetries derived from gauge theory and gravity in four-dimensional asymptotically flat spacetimes to find constraints on particle interactions in gravitational scattering and propose observational tests of general relativity in the strong gravitational fields near black holes. On the former side, we further develop a proposed holographic description of four-dimensional quantum gravity as a two-dimesional boundary theory with conformal symmetry. We derive new relations among infinite collections of symmetry constraints on the scattering of photons, gluons, and gravitons. The symmetries are characterized at tree level by a ${\rm w}_{1+\infty}$ current algebra, and correspond to an infinite series of soft theorems. We also derive general tree-level massless operator product coefficients using the two-dimensional representation of Poincar\'e symmetry and construct two-dimensional quantum states associated to four-dimensional self-dual black holes. On the observational side, we use symmetry in general relativity to uncover a pattern of alternating rings, insensitive to astrophysical details, in polarized images of black holes. The pattern provides a simple analytic model, encodes black hole spin, and could be measured with a sparse interferometric array.