Zenith Grant Awardee

Andrew Strominger

Harvard University

Project Title

Observers on the Boundary of Spacetime

Project Summary

The theories of special and general relativity have had revolutionary consequences for the physics of observers. The consequences of special relativity are well-understood. For example, while there is no absolute notion of time, a preferred notion of time can be everywhere singled out by two observers who synchronize their watches. A century after its discovery, the consequences of general relativity for the physics of observers are still not well-understood. According to seminal and surprising work in the sixties by Bondi, van der Burgh, Metzner and Sachs (BMS), the synchronization of any finite number of asymptotic observer watches still cannot single out a preferred notion of time, even in an asymptotically flat region with arbitrarily weak gravitational fields. This is known as the supertranslation ambiguity. Work in the last ten years has indicated that there is also a less-understood superrotation ambiguity implying that preferred spatial orientations or compasses cannot be everywhere established. In the last three years fundamental insights into and a proper context for these phenomena have been gained by precisely relating them to seemingly disparate phenomena from other fields: soft theorems and gravitational memory effects. The emerging coherent picture of the physics of asymptotic observers has significant implications for a variety of phenomena from QED to black holes. In this proposal we aim to investigate and clarify the implications of the still poorly-understood superrotation ambiguities on the physics of asymptotic observers.

Technical Abstract

In the last three years a concrete, coherent and many-faceted picture of a BMS supertranslation symmetry which acts on asymptotic observers near future null infinity I+ by desynchronizing their watches has emerged. The picture ties together with mathematical precision ideas from quantum field theory and general relativity as well as having applications to QED, non-abelian gauge theory and black hole information. The existence of an infinite number of associated conserved charges has been established to all orders in weak-field perturbation theory. Considerations from a number of different perspectives strongly suggest that asymptotic observers also transform under superrotations which disorient their relative spatial orientations. These superrotations generate the Virasoro group acting on the sphere at I+ but are still only poorly understood. In this project we seek to clarify the nature of superrotations and their implications. Six specific investigations towards this end are described.