Subleading BMS Charges and The Lorentz Group

TL;DR

This paper explores the extended BMS group in gravity, classifying its charges into electric and magnetic types, and relates them to multipole moments, revealing a duality that rotates boosts and rotations within the Lorentz group.

Contribution

It establishes a detailed association between subleading BMS charges, multipole moments, and Lorentz transformations, highlighting electric-magnetic duality in gravitational symmetries.

Findings

Electric and magnetic monopole moments correspond to supertranslations and dual supertranslations.

Dipole moments relate to boosts and rotations, forming the Lorentz group.

Electric-magnetic duality rotates boost and rotation generators into each other.

Abstract

The extended BMS group includes supertranslation, dual supertranslation and Lorentz transformations. The generators of these symmetries can be classified according to their parity into "electric" and "magnetic" types. Using a multipole expansion of gravitational sources in the Newman-Penrose formalism, we associate each one of these charges with a particular moment. At leading order, the "electric" and "magnetic" monopole moments correspond respectively to supertranslations and dual supertranslations. At the first subleading order, the "electric" and "magnetic" dipole moments correspond respectively to boosts and rotations, therefore comprising the entire Lorentz group. Electric-magnetic type of duality then rotates the boost and rotation generators into each other.