Part VI: Gravitational Wave Memory & BMS Symmetries
Gravitational waves leave permanent imprints on spacetime. The displacement memory effect shifts free test particles; the spin memory effect imparts a lasting velocity circulation — a gravitational holonomy sourced by angular momentum flux. Both are deeply connected to the BMS asymptotic symmetry group and soft graviton theorems, forming the celebrated infrared triangle.
Part Overview
This module develops the spin memory effect from first principles using the Bondi–Sachs formalism and the language of null infinity $\mathscr{I}^+$. We derive the Bondi–Sachs metric expansion, introduce the BMS group (supertranslations and super-rotations), review displacement memory, then derive the spin memory formula via geodesic integration and Stokes' theorem. We connect everything through the infrared triangle linking memory effects, soft theorems, and asymptotic symmetries.
The Spin Memory Effect
Physical motivation, historical context, and module roadmap
Asymptotic Expansion
Bondi–Sachs metric, news tensor, angular momentum aspect
BMS Symmetry Group
Supertranslations, super-rotations, and Noether charges
Displacement Memory
Geodesic deviation, Christodoulou nonlinear memory
Spin Memory Derivation
Velocity circulation, magnetic parity, the boxed formula
Angular Momentum Flux
Wald–Zoupas flux, unified memory table, order-of-magnitude estimates
Infrared Triangle
Subleading soft graviton theorem, Ward identity, triality
Observational Prospects
SNR formula, detector comparison, optimal sources
Key References
- Pasterski, Strominger & Zhiboedov (2016) Phys. Rev. D 93, 104016
- Strominger (2018) Lectures on the Infrared Structure of Gravity and Gauge Theory, Princeton UP
- Nichols (2017) Phys. Rev. D 95, 084048
- Wald & Zoupas (2000) Phys. Rev. D 61, 084027
- Christodoulou (1991) Phys. Rev. Lett. 67, 1486