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This work analyzes the asymptotic behaviors of the asymptotically flatsolutions of Einstein-\ae ther theory in the linear case. The vacuum solutionsfor the tensor, vector, and scalar modes are first obtained, written as sums ofvarious multipolar moments. The suitable coordinate transformations are thendetermined, and the so-called pseudo-Newman-Unti coordinate systems areconstructed for all radiative modes. In these coordinates, it is easy toidentify the asymptotic symmetries. It turns out that all three kinds of modespossess the familiar Bondi-Metzner-Sachs symmetries or the extensions as ingeneral relativity. Moreover, there also exist the \emph{subleading} asymptoticsymmetries parameterized by a time-independent vector field on a unit 2-sphere.The memory effects are also identified. The tensor gravitational wave alsoexcites similar displacement, spin, and center-of-mass memories to those ingeneral relativity. New memory effects due to the vector and scalar modesexist. The subleading asymptotic symmetry is related to the (leading) vectordisplacement memory effect, which can be viewed as a linear combination of theelectric-type and magnetic-type memory effects. However, the scalar memoryeffect seems to have nothing to do with the asymptotic symmetries at least inthe linearized theory.

Asymptotic analysis of Einstein-{\AE}ther theory and its memory effects: the linearized case