Matching conditions in locally rotationally symmetric spacetimes and radiating stars

Abstract

Abstract 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.