Self-gravitating splitting thin shells

TL;DR

This paper demonstrates that spherically symmetric thin shells with multiple matter fields are generally unstable to splitting, providing explicit examples and extending the analysis to higher-dimensional brane-world scenarios.

Contribution

It introduces a stability analysis for multi-component thin shells and constructs explicit splitting solutions, extending the results to 5D Schwarzschild-AdS spacetimes.

Findings

Thin shells with multiple matter fields are unstable to infinitesimal separation.

Explicit solutions show shells can split into two shells.

Many brane-world models are highly unstable under these conditions.

Abstract

In this paper we show that thin shells in spherically symmetric spacetimes, whose matter content is described by a pair of non-interacting spherically symmetric matter fields, generically exhibit instability against an infinitesimal separation of its constituent fields. We give explicit examples and construct solutions that represent a shell that splits into two shells. Then we extend those results for 5-dimensional Schwarzschild-AdS bulk spacetimes, which is a typical scenario for brane-world models, and show that the same kind of stability analysis and splitting solution can be constructed. We find that a widely proposed family of brane-world models are extremely unstable in this sense. Finally, we discuss possible interpretations of these features and their relation to the initial value problem for concentrated sources.