Quasi-Normal Modes of Massless Scalar Field around the 5D Ricci-flat Black String

TL;DR

This paper investigates the quasi-normal modes of a massless scalar field around a 5D Ricci-flat black string, revealing how extra dimensions and cosmological constants influence decay rates and frequencies, potentially indicating the presence of extra dimensions.

Contribution

It provides a detailed analysis of quasi-normal modes in a 5D Ricci-flat black string using WKB approximation, highlighting the effects of extra dimensions and cosmological constants.

Findings

Scalar field decays more slowly due to extra dimension and cosmological constant

Quasi-normal frequencies are affected by the quantum number n and cosmological constant

Potential observational signatures of extra dimensions in black hole physics

Abstract

As one candidate of the higher dimensional black holes, the 5D Ricci-flat black string is considered in this paper. By means of a non-trivial potential $V_{n}$, the quasi-normal modes of a massless scalar field around this black string space is studied. By using the classical third order WKB approximation, we analyse carefully the evolution of frequencies in two aspects, one is the induced cosmological constant $\Lambda$ and the other is the quantum number $n$. The massless scalar field decays more slowly because of the existences of the fifth dimension and the induced cosmological constant. If extra dimension has in fact existed near black hole, those quasi-normal frequencies may have some indication on it.