Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
arXiv:2504.12521 · doi:10.1140/epjc/s10052-025-15091-z
Abstract
These are the extended lecture notes for a minicourse presented at the I São Paulo School on Gravitational Physics discussing the Bondi--Metzner--Sachs (BMS) group, the group of symmetries at null infinity on asymptotically flat spacetimes. The BMS group has found many applications in classical gravity, quantum field theory in flat and curved spacetimes, and quantum gravity. These notes build the BMS group from its most basic prerequisites (such as group theory, symmetries in differential geometry, and asymptotic flatness) up to modern developments. These include its connections to the Weinberg soft graviton theorem, the memory effect, its use to construct Hadamard states in quantum field theory in curved spacetimes, and other ideas. Advanced sections briefly discuss the main concepts behind the infrared triangle in electrodynamics, superrotations, and the Dappiaggi--Moretti--Pinamonti group in expanding universes with cosmological horizons. New contributions by the author concerning asymptotic (conformal) Killing horizons are discussed at the end.
v4: 154 pages, 20 figures. Minor reference updates, matches published version
References in corpus (35)
- The Confrontation between General Relativity and Experiment
- The Unruh effect and its applications
- Asymptotic symmetries and subleading soft graviton theorem
- Conformal Carroll groups and BMS symmetry
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Carrollian Perspective on Celestial Holography
- The gravitational-wave memory effect
- New symmetries for the Gravitational S-matrix
- Conformal Carroll groups
- Bridging Carrollian and Celestial Holography
- The Weyl BMS group and Einstein's equations
- Null boundary phase space: slicings, news and memory
- Soft Hair as a Soft Wig
- The Asymptotic Behavior of Massless Fields and the Memory Effect
- The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
- Outlook for detecting the gravitational wave displacement and spin memory effects with current and future gravitational wave detectors
- Quantum out-states holographically induced by asymptotic flatness: Invariance under spacetime symmetries, energy positivity and Hadamard property
- Cosmological horizons and reconstruction of quantum field theories
- Gravitational Wave Memory: A New Approach to Study Modified Gravity
- Gravitational breathing memory and dual symmetries
- Killing Horizons Decohere Quantum Superpositions
- Celestial Holography: Lectures on Asymptotic Symmetries
- Symmetries of the gravitational scattering in the absence of peeling
- Quadrupolar radiation in de Sitter: Displacement memory and Bondi metric
- OGRe: An Object-Oriented General Relativity Package for Mathematica
- Local Description of Decoherence of Quantum Superpositions by Black Holes and Other Bodies
- Covariant canonical formulations of classical field theories
- Infrared finite scattering theory: Scattering states and representations of the BMS group
- Infrared finite scattering theory: Amplitudes and soft theorems
- Gravitational Wave Displacement and Velocity Memory Effects
- Lectures in Quantum Gravity
- Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group
- How to Minimize the Decoherence Caused by Black Holes
- Asymptotic dynamics and charges for FLRW spacetimes
- Null infinity as a Killing horizon