  We investigate the classical stability of Schwarzschild black hole in Jordan
and Einstein frames which are related by the conformal transformations. For
this purpose, we introduce two models of the Brans-Dicke theory and
Brans-Dicke-Weyl gravity in Jordan frame and two corresponding models in the
Einstein frame. The former model is suitable for studying the massless spin-2
graviton propagating around the Schwarzschild black hole, while the later is
designed for the massive spin-2 graviton propagating around the black hole. It
turns out that the black hole (in)stability is independent of the frame which
shows that the two frames are equivalent to each other.
