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An anisotropic standing wave braneworld and associated Sturm-Liouville problem. (English) Zbl 1235.83075

Summary: 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 of 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 with 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.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
35L05 Wave equation
83C15 Exact solutions to problems in general relativity and gravitational theory
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
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