An anisotropic standing wave braneworld and associated Sturm-Liouville problem

TL;DR

This paper derives a 5D anisotropic standing wave braneworld model with a phantom scalar field, analyzing the junction conditions and localization of fluctuations, revealing constraints on physically meaningful solutions.

Contribution

It provides a consistent derivation and physical interpretation of the anisotropic braneworld with explicit junction condition solutions and localization analysis.

Findings

Matter on the brane acts as an oscillating fluid emitting anisotropic waves.

The Sturm-Liouville problem constrains the localization of fluctuations.

Localization conditions restrict the solution space for the model.

Abstract

We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy-momentum tensor components on the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm-Liouville problem associated to the correct localization condition of the transverse to the brane metric and scalar fields. It is shown that this condition restricts the physically meaningful space of solutions for the localization of the fluctuations of the model.