Black String Perturbations in RS1 Model

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.