Rotating Black String and Effective Teukolsky Equation in Braneworld

TL;DR

This paper derives an effective Teukolsky equation for analyzing gravitational waves from rotating black strings in braneworld models, facilitating numerical studies of KK corrections and black string stability.

Contribution

It introduces a separable, effective Teukolsky equation on the brane for rotating black strings, enabling detailed gravitational wave analysis and stability studies in braneworld scenarios.

Findings

Derived a separable effective Teukolsky equation for braneworld black strings.

Formulated a master equation for the electric part of the Weyl tensor.

Facilitated numerical analysis of Kaluza-Klein corrections and Gregory-Laflamme instability.

Abstract

In the Randall-Sundrum two-brane model (RS1), a Kerr black hole on the brane can be naturally identified with a section of rotating black string. To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating black strings, we give the effective Teukolsky equation on the brane which is separable equation and hence numerically manageable. In this process, we derive the master equation for the electric part of the Weyl tensor $E_{\mu\nu}$ which would be also useful to discuss the transition from black strings to localized black holes triggered by Gregory-Laflamme instability.