Thin shell embedded in de Sitter space

TL;DR

This paper studies the properties of a static thin shell in de Sitter space, analyzing its energy, tension, and stability conditions, revealing its repulsive effects and constraints for positive mass.

Contribution

It provides a detailed analysis of the junction conditions and physical properties of a thin shell in de Sitter space, including energy, tension, and stability constraints.

Findings

Surface energy is positive; surface tension is negative at small radii.

Radial acceleration of an inner observer is repulsive.

An upper limit on shell energy ensures positive shell mass.

Abstract

The behaviour of a static thin shell embedded in dS space is investigated. To satisfy the junction conditions at the boundary, one rescales the time variable. The surface energy $\sigma$ on the shell is positive but its surface tension $\tau$ is negative when $r << a$, where $a$ is the horizon radius. The repulsive character of the radial acceleration of a static inner observer is fortified by the process of sinking in the Sitter universe. An upper limit for $\sigma$ has to be imposed for the shell mass to remain positive.