Stability of f(R) black holes
  We investigate the stability of $f(R)$ (Schwarzschild) black hole obtained from the $f(R)$ gravity. It is difficult to carry out the perturbation analysis around the black hole because the linearized Einstein equation is fourth order in $f(R)$ gravity. In order to resolve this difficulty, we transform $f(R)$ gravity into the scalar-tensor theory by introducing two auxiliary scalars.   In this case, the linearized curvature scalar becomes a scalaron, showing that all linearized equations are second order, which are the same equations for the massive Brans-Dicke theory.   It turns out that the $f(R)$ black hole is stable against the external perturbations if the scalaron does not have a tachyonic mass. 
Yun Soo Myung, Taeyoon Moon, Edwin J. Son
gr-qc hep-th