标题： 由潮汐诱导的带电物质体的多极矩 显示英文标题

标题： Tidally induced multipole moments of a charged material body

摘要： 我们定义并计算了由质量为$M$和电荷为$Q$的物质天体，因距离其$r_0$远处的一个质量为$m \ll M$且电荷为$q \ll Q$的粒子潮汐变形所产生的质量多极矩。 给定$Q/M$和$r_0$，我们选择$q/m$使得物体与粒子之间的引力吸引与静电力排斥达到平衡；这样系统就可以维持在一个静态状态。 多极矩是在允许物体自身引力较强的背景下定义的，但要求物体与其伴星之间的相互引力较弱。 在这种设定下，物体通过受潮汐常数控制的扰动度规和电磁势来用广义相对论全面描述，而相互引力则通过具有多极结构的物体在广义相对论的后牛顿近似中描述。 匹配同一场的不同描述提供了潮汐常数与多极矩之间的关系。 在我们的程序实现中，计算是在完整的爱因斯坦-麦克斯韦理论中完成的（作为未扰场的线性化扰动），无需借助后牛顿近似。 之后我们令$M/r_0$较小，并对度规以$M/r$的幂展开，从而得到多极矩及相关洛夫数。 计算针对由完美流体构成的物体进行，该流体具有均匀的电荷密度与质量密度比，并由多方方程状态控制。 我们证明了在引力和静电力量平衡的情况下，带电物体的洛夫数为负值。 即使$Q/M$非常小，这一结论仍然成立，因此我们可以得出结论：带电物体的潮汐变形性与未带电物体的截然不同，因为未带电物体的洛夫数为正值。 显示英文摘要

摘要： We define and calculate the mass multipole moments of a material body of mass $M$ and electric charge $Q$ tidally deformed by a particle of mass $m \ll M$ and charge $q \ll Q$ placed at a distance $r_0$ from the body. Given $Q/M$ and $r_0$, we choose $q/m$ so that the gravitational attraction between body and particle is balanced by the electrostatic repulsion; the system can then be maintained in a static state. The multipole moments are defined in a setting in which the body's self-gravity is allowed to be strong, but the mutual gravity between body and companion is required to be weak. In this setting, the body is described in full general relativity, in terms of a perturbed metric and electromagnetic potential characterized by tidal constants, and the mutual gravity is described within the post-Newtonian approximation to general relativity, in terms of objects with a multipole structure. Matching the different descriptions of the same field delivers a relation between the tidal constants and the multipole moments. In our implementation of this program, the calculation is performed in full Einstein-Maxwell theory (as a linearized perturbation of the unperturbed field), without appeal to a post-Newtonian approximation. After the fact we take $M/r_0$ to be small and carry out an expansion of the metric in powers of $M/r$ to obtain the multipole moments and associated Love numbers. The calculations are performed for a body made up of a perfect fluid with a uniform ratio of charge to mass densities, governed by a polytropic equation of state. We show that the Love numbers of a charged body in a situation of balanced gravitational and electrostatic forces are negative. The statement remains true even when $Q/M$ is very small, and we conclude that the tidal deformability of a charged body is radically different from that of an uncharged object, for which the Love numbers are positive.