We recast the well known Israel–Darmois matching conditions for locally rotationally symmetric (LRS-II) spacetimes using the semitetrad 1 + 1 + 2 covariant formalism. This demonstrates how the geometrical quantities including the volume expansion, spacetime shear, acceleration and Weyl curvature of two different spacetimes are related at a general matching surface inheriting the symmetry, which can be timelike or spacelike. The approach is purely geometrical and depends on matching the Gaussian curvature of two-dimensional sheets at the matching hypersurface. This also provides the constraints on the thermodynamic quantities on each spacetime so that they can be matched smoothly across the surface. As an example we regain the Santos boundary conditions and model of a radiating star matched to a Vaidya exterior in general relativity.

我们使用半四分之一1 +1 + 2协变形式论，对局部旋转对称（LRS-II）时空的著名的以色列-达莫瓦斯匹配条件进行了重铸。这证明了两个不同时空的几何量（包括体积膨胀，时空剪切，加速度和韦尔曲率）如何在继承对称性的一般匹配表面（可能是时空的）上关联的。该方法纯粹是几何方法，并且取决于在匹配的超曲面处匹配二维图纸的高斯曲率。这也对每个时空的热力学量提供了限制，因此它们可以在整个表面上平滑匹配。作为示例，我们重新获得了与广义相对论匹配的Vaidya外部的辐射恒星的Santos边界条件和模型。