论文标题
潮汐环境中紧凑的身体：新型的相对论爱情数字，以及潮汐诱发的多极力矩的牛顿后操作定义
Compact body in a tidal environment: New types of relativistic Love numbers, and a post-Newtonian operational definition for tidally induced multipole moments
论文作者
论文摘要
我们检查了一般相对论中非旋转紧凑的身体（物质或黑洞）的潮汐变形。人体的外部度量标准是通过同时扩展到身体距离和三个不同的长度尺度的比率的同时扩展的：外部时空的曲率半径，插入了身体的曲率，曲率的空间不相容性的尺度以及时间变化的尺度。该指标在人体附近的社区中是有效的，这不包括负责潮汐环境的外部物质。人体的潮汐反应封装在四种类型的相对论爱情数字中：$ k_ \ ell $，熟悉的爱情号码，衡量对静态潮汐领域的线性响应，$ p_ \ ell $，它测量了对潮汐领域的二次响应，$ \ dot {k} _ \ ell $ and $ \ ell $ \ ell $ \ ell $ \ ell $ \ e}分别是潮汐场。爱情数字通过定义潮汐引起的多极力矩获得了操作含义。以前提出的有关时刻的定义遭受了与完全度量的“纯潮汐场”减法有关的歧义。这里提出了强大的操作定义。它依赖于将人体的本地度量插入以牛顿后理论构建的全球度量中；全球指标包括负责潮汐环境的外部物质。当在牛顿后的时空中观察时，紧凑的身体是具有特定多极结构的骨架化对象。潮汐诱导的多极矩提供了该结构的描述。例如，它们在人体的潮汐加速度中表现出来，这在潮汐领域是非线性的。在潮汐互动中的领先顺序下，加速度与完全相对论计算的$ k_2 $爱情号码成正比。
We examine the tidal deformation of a nonrotating compact body (material body or black hole) in general relativity. The body's exterior metric is calculated in a simultaneous expansion in powers of the ratio between the distance to the body and three distinct length scales: the radius of curvature of the external spacetime in which the body is inserted, the scale of spatial inhomogeneity of the curvature, and the scale of temporal variation. The metric is valid in the body's immediate neighborhood, which excludes the external matter responsible for the tidal environment. The body's tidal response is encapsulated in four types of relativistic Love numbers: $k_\ell$, the familiar Love number that measures the linear response to a static tidal field, $p_\ell$, which measures the quadratic response to the tidal field, $\dot{k}_\ell$ and $\ddot{k}_\ell$, associated with first and second time derivatives of the tidal field, respectively. The Love numbers acquire an operational meaning through the definition of tidally induced multipole moments. Previously proposed definitions for the moments suffer from ambiguities associated with the subtraction of a "pure tidal field" from the full metric. A robust operational definition is proposed here. It relies on inserting the body's local metric within a global metric constructed in post-Newtonian theory; the global metric includes the external matter responsible for the tidal environment. When viewed in the post-Newtonian spacetime, the compact body appears as a skeletonized object with a specific multipole structure. The tidally induced multipole moments provide a description of this structure. They manifest themselves, for example, in the body's tidal acceleration, which is nonlinear in the tidal field. At leading order in the tidal interaction, the acceleration is proportional to the $k_2$ Love number as calculated in full general relativity.
