Quasinormal ringing of thick braneworlds with a finite extra dimension

TL;DR

This paper studies the quasinormal modes of thick branes with finite extra dimensions, revealing distinct potential shapes and mode behaviors that could help detect extra dimensions.

Contribution

It provides a comprehensive analysis of quasinormal modes in thick branes with finite extra dimensions, including new potential shapes and mode characteristics.

Findings

Identification of three potential shapes depending on parameters

Discovery of purely imaginary quasinormal modes at n=1

Potential for using quasinormal modes to detect extra dimensions

Abstract

In this work, we investigate the quasinormal modes of the Poincar\'e thick brane with a finite extra dimension. Unlike the case with an infinite extra dimension, the gravitational effective potential exhibits three distinct shapes within different ranges of the parameter $n$ in the warp factor: harmonic oscillator potential, P\"oschl-Teller potential, and volcano-like potential. We then study various types of perturbations in this system. Utilizing a combination of analytical, semi-analytical, and numerical methods, we obtain the quasinormal modes of the perturbed fields. Our findings reveal a set of discrete quasinormal modes for the thick brane, similar to those of black holes. Interestingly, when $n=1$, the quasinormal modes exhibit purely imaginary behavior. This study may provide a new way to detect the existence of extra dimensions.