The tidal problem is used to obtain the tidal deformability (or Love number) of stars. The semi-analytical study is usually treated in perturbation theory as a first order perturbation problem over a spherically symmetric background configuration consisting of a stellar interior region matched across a boundary to a vacuum exterior region that models the tidal field. The field equations for the metric and matter perturbations at the interior and exterior regions are complemented with corresponding boundary conditions. The data of the two problems at the common boundary are related by the so called matching conditions. These conditions for the tidal problem are known in the contexts of perfect fluid stars and superfluid stars modelled by a two-fluid. Here we review the obtaining of the matching conditions for the tidal problem starting from a purely geometrical setting, and present them so that they can be readily applied to more general contexts, such as other types of matter fields, different multiple layers or phase transitions. As a guide on how to use the matching conditions, we recover the known results for perfect fluid and superfluid neutron stars.

潮汐问题用于获取恒星的潮汐变形能力（或洛夫数）。半解析研究通常在微扰理论中被视为球对称背景配置上的一阶微扰问题，该背景配置由跨越边界与模拟潮汐场的真空外部区域匹配的恒星内部区域组成。内部和外部区域的度量和物质扰动的场方程由相应的边界条件补充。两个问题在公共边界处的数据通过所谓的匹配条件相关联。潮汐问题的这些条件在由双流体建模的完美流体星和超流体星的背景下是已知的。在这里，我们回顾了从纯粹的几何设置开始获得潮汐问题的匹配条件，并将它们呈现出来，以便它们可以很容易地应用于更一般的环境，例如其他类型的物质场、不同的多层或相变。作为如何使用匹配条件的指南，我们恢复了完美流体和超流体中子星的已知结果。