Title: Coupling elastic media to gravitational waves: an effective field theory approach Show Chinese title

Title: 将弹性介质与引力波耦合：有效场论方法

Abstract: The interaction of a gravitational wave (GW) with an elastic body is usually described in terms of a GW "force" driving the oscillations of the body's normal modes. However, this description is only possible for GW frequencies for which the response of the elastic body is dominated by a few normal modes. At higher frequencies the normal modes blend into a quasi-continuum and a field-theoretical description, as pioneered by Dyson already in 1969, becomes necessary. However, since the metric perturbation $h_{\mu\nu}$ is an intrinsically relativistic object, a consistent coupling to GWs can only be obtained within a relativistic (and, in fact generally covariant) theory of elasticity. We develop such a formalism using the methods of modern effective field theories, and we use it to provide a derivation of the interaction of elastic bodies with GWs valid also in the high-frequency regime, providing a first-principle derivation of Dyson's result (and partially correcting it). We also stress that the field-theoretical results are obtained working in the TT frame, while the description in terms of a force driving the normal modes is only valid in the proper detector frame. We show how to transform the results between the two frames. Beside an intrinsic conceptual interest, these results are relevant to the computation of the sensitivity of the recently proposed Lunar Gravitational Wave Antenna. Show Chinese abstract

Abstract: 引力波（GW）与弹性体的相互作用通常被描述为一种驱动物体正弦模式振荡的GW“力”。然而，这种描述仅适用于弹性体响应由少数几个正弦模式主导的GW频率。在较高频率下，正弦模式融合成准连续谱，需要场论描述，这最早可以追溯到Dyson在1969年的开创性工作。然而，由于度规扰动$h_{\mu\nu}$本质上是一个相对论对象，与GW的一致耦合只能在一个相对论（实际上是一般协变）的弹性理论框架内获得。 我们使用现代有效场论的方法发展了这种形式主义，并用它来推导弹性体与GW相互作用的结果，该结果也适用于高频范围，从而提供了Dyson结果的第一性原理推导（并在一定程度上纠正了它）。 我们还强调，场论结果是在TT坐标系中获得的，而用正弦模式驱动的力的描述仅在适当的探测器坐标系中有效。我们展示了如何在这两个坐标系之间转换结果。 除了具有内在的概念兴趣外，这些结果对于计算最近提出的月球引力波天线的灵敏度也很重要。