An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes

Abstract

We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes, obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in asymptotically flat spacetimes, thereby extending the equivalence between shockwave and soft commutators to spacetimes with non-vanishing Bondi mass. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: $(i)$ the soft supertranslation charge; $(ii)$ the shockwave effective action, or equivalently the modular Hamiltonian; and $(iii)$ the soft effective action. Finally, we compute the quantum fluctuations in the soft supertranslation charge and, assuming the supertranslation parameter may be promoted to an operator, we obtain an area law, consistent with earlier results showing that the modular Hamiltonian has such fluctuations.

39 pages; v2: Minor clarifications throughout and references added, version to appear in Journal of Physics A

References in corpus (32)

• Generalized gravitational entropy
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• BMS supertranslations and Weinberg's soft graviton theorem
• BMS charge algebra
• Local subsystems in gauge theory and gravity
• A Conformal Basis for Flat Space Amplitudes
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Conformally Soft Photons and Gravitons
• Edge modes of gravity -- I: Corner potentials and charges
• Covariant phase space with boundaries
• Infrared Divergences in QED, Revisited
• The $\Lambda$-BMS${}_4$ Charge Algebra
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Vacua of the gravitational field
• Edge modes of gravity. Part III. Corner simplicity constraints
• Asymptotic $U(1)$ charges at spatial infinity
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• Classical static final state of collapse with supertranslation memory
• Conservation and Integrability in Lower-Dimensional Gravity
• A $d$-Dimensional Stress Tensor for Mink${}_{d+2}$ Gravity
• A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity
• Modular Fluctuations from Shockwave Geometries
• Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Measuring Color Memory in a Color Glass Condensate at Electron-Ion Colliders
• From Shockwaves to the Gravitational Memory Effect
• Entanglement, Soft Modes, and Celestial Holography
• Area, Entanglement Entropy and Supertranslations at Null Infinity
• An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories

Cited by in corpus (6)

• Quantum Area Fluctuations from Gravitational Phase Space
• Modular Fluctuations in Cosmology
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• From Asymptotically Flat Gravity to Finite Causal Diamonds
• Preface to Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser
• Effective density matrix for vacua in asymptotically flat gravity