Conserved charges of the extended Bondi-Metzner-Sachs algebra
Éanna É. Flanagan, David A. Nichols
TL;DR
This work assesses whether an extended BMS symmetry, incorporating superrotations, yields well-defined classical conserved charges. It demonstrates that the standard BMS charges persist and can be complemented by finite superrotation charges, which split into electric (super center-of-mass) and magnetic (superspin) pieces, each tied to aspects of gravitational-wave memory. The authors show explicit charge formulas in nonradiative regions, analyze their behavior in stationary frames, and discuss consistency with fluxes, proposing corrections to fluxes for the extended algebra. They further connect these charges to memory observables, including ordinary, null, and spin memory, and interpret certain charges as black-hole soft hair, while acknowledging unresolved issues and the need for broader theoretical development.
Abstract
Isolated objects in asymptotically flat spacetimes in general relativity are characterized by their conserved charges associated with the Bondi-Metzner-Sachs (BMS) group. These charges include total energy, linear momentum, intrinsic angular momentum and center-of-mass location, and, in addition, an infinite number of supermomentum charges associated with supertranslations. Recently, it has been suggested that the BMS symmetry algebra should be enlarged to include an infinite number of additional symmetries known as superrotations. We show that the corresponding charges are finite and well defined, and can be divided into electric parity "super center-of-mass" charges and magnetic parity "superspin" charges. The supermomentum charges are associated with ordinary gravitational-wave memory, and the super center-of-mass charges are associated with total (ordinary plus null) gravitational-wave memory, in the terminology of Bieri and Garfinkle. Superspin charges are associated with the ordinary piece of spin memory. Some of these charges can give rise to black-hole hair, as described by Strominger and Zhiboedov. We clarify how this hair evades the no-hair theorems.