A Comment on Junction and Energy Conditions in Thin Shells

TL;DR

This paper proposes a modification to Israel's junction conditions for thin shells, clarifying the role of normal orientations and energy signs, with examples illustrating improved understanding in spherically symmetric spacetimes.

Contribution

It introduces a symmetric formulation of junction conditions that clarifies the dependence of energy signs on normal orientations, enhancing previous classifications.

Findings

Normal orientations affect energy sign calculations.

Modified formulation improves clarity of junction conditions.

Examples demonstrate the application in cosmological models.

Abstract

This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.