# Quasinormal modes of black strings in de Rham-Gabadadze-Tolley massive gravity

## TL;DR

This paper investigates the quasinormal modes of black strings in de Rham-Gabadadze-Tolley massive gravity, revealing how scalar perturbations behave and how parameters influence oscillation frequencies and decay rates.

## Contribution

It provides new analytical and numerical methods to analyze QNMs of black strings in dRGT massive gravity across different cosmological constants.

## Key findings

- Scalar modes oscillate with higher frequencies as the massive gravity parameter increases.
- No evidence of instability in neutral black strings for both positive and negative cosmological constants.
- Holographic sound poles collide and form diffusive poles as the parameter varies.

## Abstract

The effect of massive scalar perturbations on neutral black string in de Rham-Gabadadze-Tolley (dRGT) massive gravity is investigated through the study of the quasi-normal modes~(QNMs). Due to the similarity between the equation of motion of the field in the black-string and black-hole background, similar numerical and analytical techniques can be used to explore the behaviour of the QNMs. We use the asymptotic iteration method (AIM) and the WKB method to numerically calculate the QNMs of scalar perturbation in the black string background with positive cosmological constant. High-momentum behaviour of such QNMs can be analytically approximated by the first-order WKB method with excellent accuracy. For near-extremal black string with event horizon very close to the cosmological horizon, the P\"oschl-Teller technique gives accurate analytic formula for the QNMs. When massive-gravity-parameter $\gamma$ increases, we found that the scalar modes oscillate with higher frequencies and decay faster. The QNMs of black string in spacetime with negative cosmological constant are explored in all range of possible $\gamma$ using the spectral method. We found the movement of the holographic sound poles to collide and form diffusive poles as $\gamma$ changes from positive to negative values. We observe no evidence of instability of neutral black string in both positive and negative cosmological constant cases.