Abstract

Strominger and collaborators will investigate the infinitely many symmetries of nature implied by the Einstein equations for the gravitational field and discovered under the last grant cycle. These arise at the boundaries of spacetime, both at infinite light like distances and near the horizon of a rapidly spinning black hole. The theoretical research has potential applications to gravitational waves, gravitational memory, upcoming astronomical observations at the Event Horizon telescope. The Event Horizon telescope is an initiative to create observations of black holes of unparalleled resolution using an array of radio antennas located across the globe. The work supported by this award will also tackle Hawking?s black hole information paradox, which posits that information may not be conserved in a black hole. In the last few years, this group has discovered an exact triangular equivalence of three phenomena which recur ubiquitously across a wide variety of physical systems and have been separately studied for over a half century: memory, soft theorems, and asymptotic symmetries. Soft theorems in quantum field theory relate any multi-particle scattering process with the insertion of a 'soft' (i.e. low-energy) particle such as a graviton to the same process without the soft particle.

Asymptotic symmetries (such as BMS) are diffeomorphisms which act nontrivially on the physical data at infinity. The soft theorems can be derived as the quantum matrix elements of the conservation laws associated to the asymptotic symmetries. Hence they have the same physical content. The third corner of the triangle is closed by noting that The Braginsky-Thorne formula for the gravitational memory effect is precisely the Fourier transform in time of the Weinberg soft graviton theorem. There are many recurring instances of the triangle: in QED, Yang-Mills theory, gravity, in any number of dimensions, with or without supersymmetry, with leading, subleading or subsubleading soft theorems in one corner, and quantum triangles involving anomalies. This discovery of the equivalence of previously well-understood phenomena enables us to discover brand new phenomena. Given one corner of the triangle, we now know how to find the other two. This project investigates gravitational triangles. Applied to black holes, the triangular structure was shown to imply that, far from being bald featureless objects, even classical black holes carry an infinite head of 'soft hair'. The absence of any such distinguishing features was presumed in Hawking's 1975 argument for information loss, which is therefore invalidated. This insight suggests new lines of investigation into the black hole information paradox which the group will pursue. In another direction, astronomical observation suggests the existence of near-extreme Kerr black holes whose horizons spin at nearly the speed of light. General relativity implies that the dynamics of the high-redshift, near-horizon region of extreme Kerr, which includes the innermost stable circular orbit (ISCO), is governed by an infinite-dimensional emergent conformal symmetry. Symmetries of physical systems in general may both usefully characterize and have striking consequences for observational data. Precision black hole spectroscopy has advanced to the stage where astronomers are beginning to observe -- with a variety of ingenious methods -- the regions of spacetime governed by this conformal symmetry. The proposed project will undertake a systematic exploration of potential observational consequences of the conformal symmetry, in particular for the Event Horizon telescope which is already in the early stages of data collection.

Project Outcomes: The first years of this project established an exact trivalent equivalence between BMS symmetry, gravitational memory and Weinberg's soft graviton theorem. This equivalence has ramifications for classical gravitational scattering, black hole no-hair theorems and observational signals of gravitational memory which are now being explored. A major goal is to complete the half-century old program initiated by BMS and find all the symmetries of general relativity. On the observational front, we hope to find signals of the infinite-dimensional conformal symmetry which emerges near the horizon of a (near) extreme Kerr black hole. We also hope to fully understand the fascinating critical phenomena appearing at the photon ring and plan for their observation in EHT extensions. Significant and exciting progress has been made on an aspect of the research program outlined in the initial proposal, which we hope to continue in the coming year. We discovered mathematically precise and physically illuminating relations between asymptotic symmetries such as BMS, soft theorems such as Weinberg's, and gravitational memory. We demonstrated that scattering in classical GR in constrained by an infinite number of conservation laws, and that the vacuum is infinitely degenerate. This connected three disparate but well-developed fields. It brings a potentially observational component (memory) to bear on theoretical subjects and opens many avenues of investigation which have been pursued under this grant. Significant progress was made in the last year in completing the BMS program of finding all the asymptotic symmetries of GR. In particular, we found that supertranslations are the top element in a tower of asymptotic symmetries which obey the same w(1+infinity) algebra encountered in twistor theory. Last Modified: 11/29/2021 Submitted by: Andrew Strominger