# New results on the physical interpretation of black-brane gravitational perturbations

## TL;DR

This paper investigates the physical meaning of gravitational perturbations in anti-de Sitter black branes, clarifying whether certain modes cause mass variation or generate gravitational waves, using gauge-invariant methods and Weyl scalar analysis.

## Contribution

It provides a detailed analysis of black-brane perturbations with arbitrary wave number, resolving controversy over their physical interpretation through gauge-invariant and Weyl scalar techniques.

## Key findings

- Polar zero wave number perturbations can cause gravitational waves.
- Axial perturbations induce slow rotation in black branes.
- The study clarifies the physical effects of different perturbation modes.

## Abstract

The linear perturbation theory applied to the study of black holes is a traditional and powerful tool to investigate some of the basic properties of these objects, such as the stability of the event horizon, the spectra of quasinormal modes, the scattering and the production of waves in a process of gravitational collapse. Since long ago, the physical interpretation of the linear fluctuations in the metric of spherically symmetric black holes has been established. In a multipolar expansion, it is known that polar perturbations of a monopole type ($l=0$) can only increase the black-hole mass, axial perturbations of a dipole type ($l=1$) induce a slow rotation in the system, and perturbations with $l\geq 2$ always lead to the production of gravitational waves. However, in relation to the planar Schwarzschild anti--de Sitter black holes (or black branes, for short), there is still no conclusive study on some aspects of the physical meaning of these perturbations. In particular, there is some controversy concerning the polar sector of fluctuations with zero wave number $(k=0)$. Some authors claim that this kind of perturbations causes only a variation in the black-brane mass parameter, while others obtained also evidence for the existence of gravitational waves associated to such modes. The present study aims to contribute to the resolution of this controversy by revealing the physical meaning of the gravitational perturbations of anti--de Sitter black branes. In this work we use the Chandrasekhar's gauge formalism to evaluate the linear variations in the complex Weyl scalars in terms of the Regge-Wheeler-Zerilli gauge-invariant quantities. Then we use the Szekeres' proposal for the meaning of the Weyl scalars and the Pirani's criterion for the existence of gravitational radiation in order to give a physical interpretation of the black-brane perturbations with arbitrary wave number value.