# Sound modes and stability of momentum dissipated black branes in holography

## TL;DR

This paper analyzes sound modes and stability in momentum dissipated holographic systems, specifically Einstein-linear axions and Einstein-Maxwell-dilaton-axion theories, revealing their sound velocities, attenuation, and conditions for instability.

## Contribution

It provides analytical and numerical analysis of sound modes in two holographic models with momentum dissipation, including stability conditions and comparison with known black hole solutions.

## Key findings

- Sound velocities match those of BTZ black holes in certain cases.
- Analytical and numerical dispersion relations agree.
- Dynamical instability occurs when the null energy condition is violated.

## Abstract

We systematically investigate the sound modes of momentum dissipated holographic systems. In particular, we focus on the Einstein-linear axions and the Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetime dimensions. The sound velocities of the two theories are computed respectively and the sound attenuation of the Einstein-Maxwell-axion theory is also calculated analytically. We also obtain numeral dispersion relations in the two theories which match with our analytical results. Our results show that the sound velocity of the Einstein-Maxwell-dilaton theory with additional linear axion fields is equivalent to that of 2 + 1 - dimensional Banados-Teitelboim-Zanelli black holes. It allowed us to compare our solution of the Einstein-linear axions theory with that of systems without translational invariance from another method. After the computation on the sound velocity, we calculate the quasinormal modes of scalar-type fluctuations in the Einstein-Maxwell-dilaton-axion theory. The results show that a dynamical instability is observed under the condition that the null energy condition is violated.