标题： 爱因斯坦-Æther理论及其记忆效应的渐近分析：线性化情况 显示英文标题

标题： Asymptotic analysis of Einstein-Æther theory and its memory effects: the linearized case

摘要： 这项工作分析了爱因斯坦-\ae 理论在线性情况下的渐近平坦解的渐近行为。 张量、矢量和标量模式的真空解首先被获得，写成各种多极矩的和。 然后确定了合适的坐标变换，并为所有辐射模式构建了所谓的伪纽曼-翁蒂坐标系。 在这些坐标中，很容易识别渐近对称性。 结果表明，这三种模式都具有熟悉的邦迪-梅茨纳-萨克斯对称性或广义相对论中的扩展形式。 此外，还存在由单位2球面上的时间无关向量场参数化的\emph{次优} 渐近对称性。 记忆效应也被识别出来。 张量引力波也会激发类似于广义相对论中的位移、自旋和质心记忆效应。 由于矢量和标量模式存在新的记忆效应。 次级渐近对称性与（主导）矢量位移记忆效应相关，这可以看作是电型和磁型记忆效应的线性组合。 然而，标量记忆效应似乎至少在线性化理论中与渐近对称性无关。 显示英文摘要

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