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 [1] and Rainer K. Sachs [2] 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.[3] 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.[4] As a result, and following proposals according to which asymptotic symmetries could explain the microscopic origin of black hole entropy,[5] BMS symmetry and its gauge-theoretic cousins are a subject of active research as of May 2020.
References
- Bondi, H.; Van der Burg, M.G.J.; Metzner, A. (1962). "Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems". Proceedings of the Royal Society of London A. A269: 21–52. doi:10.1098/rspa.1962.0161.
- Sachs, R. (1962). "Asymptotic symmetries in gravitational theory". Physical Review. 128: 2851–2864. doi:10.1103/PhysRev.128.2851.
- Barnich, Glenn; Troessaert, Cédric (2010). "Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited". Physical Review Letters. 105. arXiv:0909.2617. doi:10.1103/PhysRevLett.105.111103.
- Strominger, Andrew (2017). "Lectures on the Infrared Structure of Gravity and Gauge Theory". arXiv:1703.05448. Cite journal requires
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(help) - Hawking, Stephen; Perry, Malcolm; Strominger, Andrew (2016). "Soft Hair on Black Holes". Physical Review Letters. 116. arXiv:1601.00921. doi:10.1103/PhysRevLett.116.231301.