Reconsideration of the Regge-Wheeler equation
  Reconsideration of the Regge-Wheeler equation is processed by using the Painlev\'{e} coordinate and "good" timelier to define the initial time. We find that: the Regge-Wheeler equation could has positive imaginary frequency. Because the Regge-Wheeler equation is the odd (angular) perturbation to the Schwarzschild black hole, the conclusion is that the Schwarzschild black hole is unstable with respect to the rotating perturbation. 
Guihua Tian, Shikun Wang, and Zhao Zheng