Restudy of the stability problem of the Schwarzschild black hole

The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole (r>2 m) and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.