Matching conditions in Locally Rotationally Symmetric spacetimes and radiating stars

TL;DR

This paper reformulates the Israel-Darmois matching conditions for LRS-II spacetimes using a covariant formalism, linking geometrical and thermodynamic quantities at the matching surface, and applies it to model a radiating star with Vaidya exterior.

Contribution

It introduces a purely geometrical covariant approach to matching conditions in LRS-II spacetimes, unifying geometric and thermodynamic constraints, and demonstrates its application to radiating star models.

Findings

Reformulation of matching conditions using covariant formalism.

Derivation of constraints on thermodynamic quantities for smooth matching.

Application to radiating star matched to Vaidya exterior.

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 2-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.