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

TL;DR

This paper demonstrates that in diffeomorphism-invariant gravity theories with tensor modes, the asymptotic symmetry group includes the BMS group, and tensor gravitational waves induce displacement, spin, and center-of-mass memory effects linked to the shear tensor.

Contribution

It establishes a general property of tensor gravitational memory effects across a broad class of gravity theories, including those breaking Lorentz symmetry.

Findings

Asymptotic symmetry group contains the BMS group in these theories.

Tensor gravitational waves induce measurable memory effects.

Memory effects depend on the asymptotic shear tensor.

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.