Bondi–Metzner–Sachs group

The Bondi–Metzner–Sachs (BMS) group is an asymptotic symmetry group of asymptotically flat, Lorentzian spacetimes at null (i.e. light-like) infinity. It was originally proposed in 1962 by Hermann Bondi, M. G. van der Burg, A. W. Metzner and Rainer K. Sachs in order to investigate the flow of energy at infinity due to propagating gravitational waves.

Abstractly, the BMS group is an infinite-dimensional extension of the Poincaré group, and shares a similar structure: just as the Poincaré group is a semidirect product between the Lorentz group and the Abelian vector group of space-time translations, the BMS group was originally defined as a semidirect product of the Lorentz group with an infinite-dimensional Abelian group of so-called supertranslations. As of May 2020, this definition is a subject of debate, since various further extensions have been proposed in the literature—most notably one where the Lorentz group is also extended into an infinite-dimensional group of so-called superrotations. The enhancement of space-time translations into infinite-dimensional supertranslations is now considered a key feature of BMS symmetry, partly owing to the fact that imposing supertranslation invariance on S-matrix elements involving gravitons yields Ward identities that turn out to be equivalent to Weinberg's soft graviton theorem. In fact, such a relation between asymptotic symmetries and soft theorems is not specific to gravitation alone, but is rather a general property of gauge theories. As a result, and following proposals according to which asymptotic symmetries could explain the microscopic origin of black hole entropy, BMS symmetry and its gauge-theoretic cousins are a subject of active research as of May 2020.