nLab Bondi-Metzner-Sachs group

Idea

The Bondi-Metzner-Sach group (BMS group) is the group of asymptotic symmetries of asymptotically flat spacetimes at lightlike infinity.

References

Named after:

• Hermann Bondi, M. G. J. Van der Burg, A. W. K. Metzner: Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system, Proceedings of the Royal Society A 269 1336 [doi:10.1098/rspa.1962.0161]

• Rainer K. Sachs: Asymptotic Symmetries in Gravitational Theory, Phys. Rev. 128 (1962) 2851 [doi:10.1103/PhysRev.128.2851]

Lecture notes and introductions:

• Níckolas de Aguiar Alves: Lectures on the Bondi–Metzner–Sachs group and related topics in infrared physics, Eur. Phys. J. C 86 5 (2026) 507 [arXiv:2504.12521, doi:10.1088/1361-6404/ae4951]

• Simone Speziale: A short introduction to boundary symmetries [arXiv:2512.16810]

• Xavier Bekaert, Yannick Herfray, Lea Mele, Noémie Parrini: A geometrical invitation to BMS group theory [arXiv:2602.12965]

In relation to the Wheeler-DeWitt equation:

• Marc Henneaux: Wheeler-DeWitt equation and Bondi-Metzner-Sachs (BMS) symmetry [arXiv:2506.02240]

Similar symmetries of near horizon geometries of black hole spacetimes (with higher curvature corrections):

• Mariano Chernicoff, Gaston Giribet, Julio Oliva: Higher-curvature corrections and near horizon symmetries [arXiv:2506.21747]

See also:

• Ratindranath Akhoury, Arielle Schutz, David Garfinkle: Superrotations are Linkages [arXiv:2507.04245]

• Yu-fan Zheng: Supersymmetric $BMS_4$ Algebras Revisited: Electric/Magnetic Superalgebras and Free Field Realization [arXiv:2508.17925]

• Xavier Bekaert, Laura Donnay, Yannick Herfray: BMS particles [arXiv:2412.06002]

• Romain Ruzziconi, Peter West: Extended BMS representations and strings [arXiv:2601.00662]

• Geoffrey Compère, Sébastien Robert: Conservation law of super-Lorentz charges [arXiv:2606.26848]

• Diego Hidalgo, Stefan Vandoren, Huaxuan Zeng: $BMS_3$ invariant field theories [arXiv:2607.06826]