On the thin wall limit of thick planar domain walls

TL;DR

This paper investigates the thin wall limit of thick planar domain walls in gravitating systems, showing how junction conditions transition from thick to thin wall descriptions within general relativity.

Contribution

It demonstrates that Darmois junction conditions for thick walls reduce to Israel junction conditions in the thin wall limit, clarifying the connection between these formalisms.

Findings

Darmois conditions reproduce Israel conditions in the thin wall limit

The transition from thick to thin wall formalism is explicitly demonstrated

Provides a consistent framework for modeling domain walls in gravity

Abstract

Considering a planar gravitating thick domain wall of the $\lambda \phi^4$ theory, we demonstrate how the Darmois junction conditions written on the boundaries of the thick wall with the embedding spacetimes reproduce the Israel junction condition across the wall when one takes its thin wall limit.