Mass inflation in f(R) gravity: A conjecture on the resolution of the
  mass inflation singularity
  We study gravitational collapse of a charged black hole in f(R) gravity using
double-null formalism. We require cosmological stability to f(R) models; we
used the Starobinsky model and the R + (1/2)cR^2 model. Charged black holes in
f(R) gravity can have a new type of singularity due to higher curvature
corrections, the so-called f(R)-induced singularity, although it is highly
model-dependent. As the advanced time increases, the internal structure will
approach the Cauchy horizon, which may not be an inner apparent horizon. There
is mass inflation as one approaches the Cauchy horizon and hence the Cauchy
horizon may be a curvature singularity with nonzero area. However, the Ricci
scalar is finite for an out-going null observer. This can be integrated as
follows: Cosmologically stable higher curvature corrections of the Ricci scalar
made it bounded even in the presence of mass inflation. Finally, we conjecture
that if there is a general action including general higher curvature
corrections with cosmological stability, then the corrections can make all
curvature components finite even in the presence of mass inflation. This might
help us to resolve the problem of inner horizon instability of regular black
hole models.
