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In this paper, we explore the interior dynamics of neutral and charged blackholes in $f(R)$ gravity. We transform $f(R)$ gravity from the Jordan frame intothe Einstein frame and simulate scalar collapses in flat, Schwarzschild, andReissner-Nordstr\"om geometries. In simulating scalar collapses inSchwarzschild and Reissner-Nordstr\"om geometries, Kruskal and Kruskal-likecoordinates are used, respectively, with the presence of $f'$ and a physicalscalar field being taken into account. The dynamics in the vicinities of thecentral singularity of a Schwarzschild black hole and of the inner horizon of aReissner-Nordstr\"om black hole is examined. Approximate analytic solutions fordifferent types of collapses are partially obtained. The scalar degree offreedom $\phi$, transformed from $f'$, plays a similar role as a physicalscalar field in general relativity. Regarding the physical scalar field in$f(R)$ case, when $d\phi/dt$ is negative (positive), the physical scalar fieldis suppressed (magnified) by $\phi$, where $t$ is the coordinate time. For darkenergy $f(R)$ gravity, inside black holes, gravity can easily push $f'$ to $1$.Consequently, the Ricci scalar $R$ becomes singular, and the numericalsimulation breaks down. This singularity problem can be avoided by adding an$R^2$ term to the original $f(R)$ function, in which case an infinite Ricciscalar is pushed to regions where $f'$ is also infinite. On the other hand, incollapse for this combined model, a black hole, including a centralsingularity, can be formed. Moreover, under certain initial conditions, $f'$and $R$ can be pushed to infinity as the central singularity is approached.Therefore, the classical singularity problem, which is present in generalrelativity, remains in collapse for this combined model.

Interior dynamics of neutral and charged black holes in f(R) gravity