The General Property of the Tensor Gravitational Memory Effect in Theories of Gravity: The Linearized Case

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. These asymptotic symmetries preserve the causal structure of the tensor degrees of freedom. They possess the displacement, spin and center-of-mass memory effects. These effects 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.