Gravitational memory and Ward identities in the local detector frame

TL;DR

This paper reformulates gravitational memory effects in local detector frames, linking them to residual diffeomorphisms and BMS symmetries, and derives related Ward identities and soft theorems applicable to gravitational wave observations.

Contribution

It provides an equivalent local coordinate description of gravitational memory, connecting residual diffeomorphisms to BMS symmetries and deriving new Ward identities in this framework.

Findings

Memory encoded in large residual diffeomorphisms in TT gauge

Derived Ward identities and soft theorems for local detectors

Validated identities for planar gravitational waves

Abstract

Gravitational memory, which describes the permanent shift in the strain after the passage of gravitational waves, is directly related to Weinberg's soft graviton theorems and the Bondi-Metzner-Sachs (BMS) symmetry group of asymptotically flat space-times. In this work, we provide an equivalent description of the phenomenon in local coordinates around gravitational wave detectors, such as transverse-traceless (TT) gauge. We show that gravitational memory is encoded in large residual diffeomorphisms in this gauge, which include time-dependent anisotropic spatial rescalings, and prove their equivalence to BMS transformations when translated to TT gauge. We then derive the associated Ward identities and associated soft theorems, for both scattering amplitudes and equal-time (in-in) correlation functions, and explicitly check their validity for planar gravitational waves. The in-in identities are recognized as the flat-space analog of the well-known inflationary consistency relations.