Topics In General Relativity

Harvard University, Cambridge MA

Investigators

Abstract

The PI's group will push forward at the boundaries of our understanding of both classical and quantum aspects of Einstein's theory of general relativity. The overarching goal is to find a way to describe the gravitational force in terms of quantum mechanics: two fields that have resisted unification for more than a century. The projects described here build on a recent synthesis of long-established techniques developed in the study of soft theorems by particle theorists and in the study by relativists of the asymptotic boundaries of spacetime. This synthesis has ignited a fertile collaboration between physicists in disparate fields from twistor theory to LIGO to string theory. It has led to both new experimental predictions (of novel memory effects) and new concrete insights into spacetime as a quantum theory on the celestial sphere as presciently hypothesized long ago by Newman and Penrose and recently reincarnated as the holographic principle. This enterprise in being driven by an unusually diverse and young group of theoretical physicists. Strominger and collaborators will continue their investigation of the infinitely many nontrivially- acting exact symmetries implied by the Einstein equations. These arise in the deep infrared, both in asymptotically flat spacetimes at null infinity – where they are beautifully and powerfully recast as symmetries of the celestial sphere – and near the horizon of a black hole. This theoretical research has potential implications for gravitational scattering, gravitational memory, upcoming observations at the Event Horizon Telescope (EHT), and the black hole information paradox. They will further develop the powerful and exact triangular equivalence of three ubiquitous phenomena: memory, soft theorems, and asymptotic symmetries. Soft theorems in quantum field theory relate multi-particle scattering process with and without insertions of “soft” (low-energy) particles, such as gravitons. Asymptotic symmetries (such as BMS) are diffeomorphisms that act nontrivially on the physical data at infinity. Soft theorems can be derived as quantum matrix elements of conservation laws associated to the asymptotic symmetries, and are the Fourier transform of the formula for the gravitational memory effect. This research program will develop the many recurring instances of this triangular equivalence in both gravity and gauge theory. They intend to answer the central question of how to enumerate all the non- trivial asymptotic symmetries of general relativity in four asymptotically flat spacetime dimensions. In the past grant cycle, it was shown that gravitational scattering amplitudes can be recast as conformal correlators on the celestial sphere at null infinity, where the powerful tools of two-dimensional conformal field theory can be exploited, bringing a complete understanding of the nontrivial asymptotic symmetries within future reach. Very recently it was that physically observable symmetries organize into the group known as w(1+infinity), a significant step that provides direct connections to twistor theory. Applied to black holes, the triangular structure implies that, far from being bald featureless objects, even classical black holes carry an infinite head of “soft hair.” This insight has led to new lines of inquiry into the black hole information paradox. Observational signatures of various Kerr black hole symmetries will be investigated. General relativity implies that the dynamics of the near-horizon region of extreme Kerr and light rays near the photon ring of any Kerr black hole both display conformal scaling symmetries. Advances in precision black hole imaging are beginning to allow astronomers to observe the regions of spacetime governed by these symmetries, and the project will explore their potential observational consequences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.