Gravitational memory and soft theorems: The local perspective

Valerio De Luca; Justin Khoury; Sam S. C. Wong

doi:10.1103/gbg1-mz49

Gravitational memory and soft theorems: The local perspective

Valerio De Luca^*
, Justin Khoury^*
, Sam S. C. Wong^*

^*Corresponding author for this work

Department of Physics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

25 Downloads (CityUHK Scholars)

Abstract

In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. These relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators. © 2025 American Physical Society

Original language	English
Article number	L021502
Journal	Physical Review D
Volume	112
Issue number	2
Online published	14 Jul 2025
DOIs	https://doi.org/10.1103/gbg1-mz49
Publication status	Published - Jul 2025

Funding

We thank D. Nichols for interesting discussions, and an anonymous referee for valuable comments regarding loop-order corrections to the soft theorems for scattering amplitudes. V. D. L. is supported by funds provided by the Center for Particle Cosmology at the University of Pennsylvania. The work of J. K. is supported in part by the DOE (HEP) Award No. DESC0013528. The work of S.. W. is supported by APRCCityU New Research Initiatives/Infrastructure Support from Central.

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: De Luca, V., Khoury, J., & Wong, S. S. C. (2025). Gravitational memory and soft theorems: The local perspective. Physical Review D, 112(2), Article L021502. https://doi.org/10.1103/gbg1-mz49 The copyright of this article is owned by American Physical Society.

Access Output

10.1103/gbg1-mz49

303219787.pdfFinal Published version, 353 KB

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{43321f5002114b62ba03b69ff5585b7a,

title = "Gravitational memory and soft theorems: The local perspective",

abstract = "In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. These relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators. {\textcopyright} 2025 American Physical Society",

author = "\{De Luca\}, Valerio and Justin Khoury and Wong, \{Sam S. C.\}",

year = "2025",

month = jul,

doi = "10.1103/gbg1-mz49",

language = "English",

volume = "112",

journal = "Physical Review D",

issn = "2470-0010",

publisher = "American Physical Society",

number = "2",

}

TY - JOUR

T1 - Gravitational memory and soft theorems

T2 - The local perspective

AU - De Luca, Valerio

AU - Khoury, Justin

AU - Wong, Sam S. C.

PY - 2025/7

Y1 - 2025/7

N2 - In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. These relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators. © 2025 American Physical Society

AB - In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. These relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators. © 2025 American Physical Society

U2 - 10.1103/gbg1-mz49

DO - 10.1103/gbg1-mz49

M3 - RGC 21 - Publication in refereed journal

SN - 2470-0010

VL - 112

JO - Physical Review D

JF - Physical Review D

IS - 2

M1 - L021502

ER -

Gravitational memory and soft theorems: The local perspective

Abstract

Funding

Publisher's Copyright Statement

Access Output

Other Access Options

Permanent Link

Fingerprint

Cite this