Black String Perturbations in RS1 Model

TL;DR

This paper develops a formalism to analyze black string perturbations in the RS1 model, deriving effective equations and discussing implications for gravitational waves and stability.

Contribution

It introduces a general formalism for black string perturbations in RS1, deriving the master and effective Teukolsky equations at low energy.

Findings

Effective Teukolsky equation for gravitational waves

Analysis of Gregory-Laflamme instability effects

Formalism applicable to perturbed rotating black strings

Abstract

We present a general formalism for black string perturbations in Randall-Sundrum 1 model (RS1). First, we derive the master equation for the electric part of the Weyl tensor $E_{\mu\nu}$. Solving the master equation using the gradient expansion method, we give the effective Teukolsky equation on the brane at low energy. It is useful to estimate gravitational waves emitted by perturbed rotating black strings. We also argue the effect of the Gregory-Laflamme instability on the brane using our formalism.