Self-gravitating splitting thin shells

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.

18 pages, 3 figures

References in corpus (3)

• Brane-World Gravity
• On the dynamics of thin shells of counter rotating particles
• Static spherically symmetric Einstein-Vlasov shells made up of particles with a discrete set of values of their angular momentum

Cited by in corpus (2)

• Vacuum thin shells in Einstein-Gauss-Bonnet brane-world cosmology
• Thermodynamic instability of splitting thin shell solutions in braneworld Einstein-Gauss-Bonnet gravity