Rotating black string and the effective Teukolsky equation in the braneworld

In the Randall-Sundrum two-brane (RS1) model, a large Kerr black hole on the brane can be naturally identified with a section of a 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 a separable equation and hence numerically manageable. In this process, we derive the master equation for the electric part of the Weyl tensor, E_μν, which is also useful in discussing the transition from black strings to localized black holes triggered by Gregory-Laflamme instability.