Conserved charges of the extended Bondi-Metzner-Sachs algebra

TL;DR

This paper extends the BMS algebra in general relativity to include superrotations, defining finite charges associated with these symmetries, and explores their implications for gravitational memory and black hole hair.

Contribution

It demonstrates that superrotation charges are finite and well-defined, expanding the BMS algebra and linking these charges to gravitational memory effects and black hole hair.

Findings

Superrotation charges are finite and well-defined.

Supermomentum and super center-of-mass charges relate to gravitational memory.

Some charges can give rise to black-hole hair.

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.