  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory