Black hole stability in Jordan and Einstein frames

Abstract: 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.