  Spherical scalar collapse in f(R) gravity is studied numerically in
double-null coordinates in the Einstein frame. Dynamics in the vicinity of the
singularity of the formed black hole is examined via mesh refinement and
asymptotic analysis. Before the collapse, the scalar degree of freedom f' is
coupled to a physical scalar field, and general relativity is restored. During
the collapse, the major energy of the physical scalar field moves to the
center. As a result, f' loses the coupling and becomes light, and gravity
transits from general relativity to f(R) gravity. Due to strong gravity from
the singularity and the low mass of f', f' will cross the minimum of the
potential and approach zero. Therefore, the dynamical solution is significantly
different from the static solution of the black hole in f(R) gravity---it is
not the de Sitter-Schwarzschild solution as one might have expected. f' tries
to suppress the evolution of the physical scalar field, which is a dark energy
effect. As the singularity is approached, metric terms are dominant over other
terms. The Kasner solution for spherical scalar collapse in f(R) theory is
obtained and confirmed by numerical results. These results support the
Belinskii-Khalatnikov-Lifshitz conjecture well.
