Braneworld resonances

TL;DR

This paper analyzes gravitational wave resonances in a braneworld model with a Schwarzschild-anti-de Sitter bulk, revealing a variety of quasi-normal modes and their potential implications for cosmology.

Contribution

It provides a detailed analysis of tensor-mode perturbations and quasi-normal modes in a generalized braneworld setup, extending previous work to include generic matter content.

Findings

Identification of quasi-normal mode frequencies and lifetimes.

Discovery of lightly damped quasi-bound states.

Recovery of 4D general relativity zero-mode on large branes.

Abstract

We investigate in detail gravitational waves in an Schwarzschild-anti-de Sitter bulk spacetime surrounded by an Einstein static brane with generic matter content. Such a model provides a useful analogy to braneworld cosmology at various stages of its evolution, and generalizes our previous work [gr-qc/0504023] on pure tension Einstein-static branes. We find that the behaviour of tensor-mode perturbations is completely dominated by quasi-normal modes, and we use a variety of numeric and analytic techniques to find the frequencies and lifetimes of these excitations. The parameter space governing the model yields a rich variety of resonant phenomena, which we thoroughly explore. We find that certain configurations can support a number of lightly damped `quasi-bound states'. A zero-mode which reproduces 4-dimensional general relativity is recovered on infinitely large branes. We also examine the problem in the time domain using Green's function techniques in addition to direct numeric integration. We conclude by discussing how the quasi-normal resonances we find here can impact on braneworld cosmology.