Gravitational Waves from Rotating Black Strings

TL;DR

This paper develops a separable Teukolsky equation to estimate Kaluza-Klein corrections to gravitational waves emitted by rotating black strings in the Randall-Sundrum model, aiding understanding of black string stability and black hole transitions.

Contribution

It derives a separable effective Teukolsky equation on the brane for rotating black strings, facilitating numerical analysis of KK corrections and black string stability.

Findings

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

Provided a separable Teukolsky equation for gravitational wave analysis.

Discussed implications for black string stability and black hole transitions.

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.