Editing General relativity (section)

=== Asymptotic symmetries ===
{{Main|Bondi–Metzner–Sachs group}}
The spacetime symmetry group for [[special relativity]] is the [[Poincaré group]], which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries, if any, might apply in General Relativity. A tractable case might be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, ''viz.'', the Poincaré group.

In 1962 [[Hermann Bondi]], M. G. van der Burg, A. W. Metzner<ref name="bondi etal 1962">{{cite journal|title=Gravitational waves in general relativity: VII. Waves from axisymmetric isolated systems|journal= Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume=269|pages=21–52|doi=10.1098/rspa.1962.0161|year=1962|last1=Bondi|first1=H.|last2=Van der Burg|first2=M.G.J.|last3=Metzner|first3=A.|issue=1336|bibcode=1962RSPSA.269...21B|s2cid=120125096}}</ref> and [[Rainer K. Sachs]]<ref name=sachs1962>{{cite journal|title=Asymptotic symmetries in gravitational theory|journal=Physical Review|volume=128|pages=2851–2864|doi=10.1103/PhysRev.128.2851|year=1962|last1=Sachs|first1=R.|issue=6|bibcode=1962PhRv..128.2851S}}</ref> addressed this [[Bondi–Metzner–Sachs group|asymptotic symmetry]] problem in order to investigate the flow of energy at infinity due to propagating [[gravitational wave]]s. Their first step was to decide on some physically sensible boundary conditions to place on the gravitational field at light-like infinity to characterize what it means to say a metric is asymptotically flat, making no ''a priori'' assumptions about the nature of the asymptotic symmetry group—not even the assumption that such a group exists. Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations that leave invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. What they found was that the asymptotic symmetry transformations actually do form a group and the structure of this group does not depend on the particular gravitational field that happens to be present. This means that, as expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field at least at spatial infinity. The puzzling surprise in 1962 was their discovery of a rich infinite-dimensional group (the so-called BMS group) as the asymptotic symmetry group, instead of the finite-dimensional Poincaré group, which is a subgroup of the BMS group. Not only are the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as ''supertranslations''. This implies the conclusion that General Relativity (GR) does ''not'' reduce to special relativity in the case of weak fields at long distances. It turns out that the BMS symmetry, suitably modified, could be seen as a restatement of the universal [[soft graviton theorem]] in [[quantum field theory]] (QFT), which relates universal infrared (soft) QFT with GR asymptotic spacetime symmetries.<ref name=strominger2017>{{cite arXiv|title=Lectures on the Infrared Structure of Gravity and Gauge Theory|eprint=1703.05448|year=2017|last1=Strominger|first1=Andrew|class=hep-th|quote=...redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. To be published Princeton University Press, 158 pages.}}</ref>