BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (
 $$ \mathrm{\mathcal{I}} $$
 +). BMS− transformations similarly act on ingoing data at past null infinity (
 $$ \mathrm{\mathcal{I}} $$
 −). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link $$ \mathrm{\mathcal{I}} $$
 + to $$ \mathrm{\mathcal{I}} $$
 − and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity $$ \mathcal{S} $$
 -matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S
 2 at $$ \mathrm{\mathcal{I}} $$
 . The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of $$ \mathrm{\mathcal{I}} $$
 .

/pdf/on-bms-invariance-of-gravitational-scattering-1d9o0kzu76.pdf

On BMS Invariance of Gravitational Scattering

The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed. First the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities are recalled. Then the various specific constructions and their properties (both successes and defects) are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned. This review is based on the talks given at the Erwin Schrodinger Institute, Vienna, in July 1997, at the Universitat Tubingen, in May 1998, and at the National Center for Theoretical Sciences in Hsinchu and at the National Central University, Chungli, Taiwan, in July 2000.

/pdf/quasi-local-energy-momentum-and-angular-momentum-in-gr-a-2ickuhcmd5.pdf

Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

/pdf/quasi-local-energy-momentum-and-angular-momentum-in-general-wmf4x6598j.pdf

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity.

Asymptotic symmetries at future null infinity (
 $$ \mathrm{\mathcal{I}} $$
 +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through $$ \mathrm{\mathcal{I}} $$
 + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are “large” gauge transformations which approach locally holomorphic functions on the conformal two-sphere at $$ \mathrm{\mathcal{I}} $$
 + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of $$ \mathrm{\mathcal{I}} $$
 +. The current Ward identities include Weinberg’s soft photon theorem and its colored extension.

/pdf/asymptotic-symmetries-of-yang-mills-theory-2d1kwwtqk8.pdf

Asymptotic symmetries of Yang-Mills theory

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

David G. Blair

Papers

Gravitational waves in general relativity