The general property of the tensor gravitational memory effect in theories of gravity

TL;DR

The paper proves a universal feature: in any diffeomorphism-invariant gravity theory with tensor degrees of freedom propagating at a constant, isotropic speed, the asymptotic symmetry group near isolated systems is the (extended/generalized) BMS group, and tensor gravitational memory (displacement, spin, CM) is governed by the asymptotic shear. Using a linearized, model-independent quadratic action for the tensor sector and a disformal transformation to an unphysical metric, the authors show the tensor memory effects are vacuum transitions parameterized by supertranslations, with the tensor GW speed denoted as $s_2$ and Lorentz invariance recovered when $s_2=1$. The analysis generalizes known results from GR, Brans-Dicke, dynamical Chern-Simons, and Einstein-æther theories and remains valid even when Lorentz symmetry is broken by a timelike direction, though nonlinear corrections are required to derive flux-balance laws and associated soft theorems. The work further discusses possible generalizations to Lorentz-violating frameworks and higher-derivative theories, arguing that, under certain conditions, the same asymptotic symmetry and memory structure persists, while dispersion and extra modes may appear in more exotic scenarios.

Abstract

In this work, it is shown that based on the linear analysis, as long as a theory of gravity is diffeomorphism invariant and possesses the tensor degrees of freedom propagating at a constant, isotropic speed without dispersion, its asymptotic symmetry group of an isolated system contains the (extended/generalized) Bondi-Metzner-Sachs group. The tensor gravitational wave induces the displacement, spin and center-of-mass memory effects. They depend on the asymptotic shear tensor. The displacement memory effect is the vacuum transition and parameterized by a supertranslation transformation. All of these hold even when the Lorentz symmetry is broken by a special timelike direction.