  We study responses of the Brans-Dicke field due to gravitational collapses of
scalar field pulses using numerical simulations. Double-null formalism is
employed to implement the numerical simulations. If we supply a scalar field
pulse, it will asymptotically form a black hole via dynamical interactions of
the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke
field by two different regions. First, we observe the late time behaviors after
the gravitational collapse, which include formations of a singularity and an
apparent horizon. Second, we observe the fully dynamical behaviors during the
gravitational collapse and view the energy-momentum tensor components. For the
late time behaviors, if the Brans-Dicke coupling is greater (or smaller) than
-1.5, the Brans-Dicke field decreases (or increases) during the gravitational
collapse. Since the Brans-Dicke field should be relaxed to the asymptotic value
with the elapse of time, the final apparent horizon becomes time-like (or
space-like). For the dynamical behaviors, we observed the energy-momentum
tensors around $\omega$ ~ -1.5. If the Brans-Dicke coupling is greater than
-1.5, the $T_{uu}$ component can be negative at the outside of the black hole.
This can allow an instantaneous inflating region during the gravitational
collapse. If the Brans-Dicke coupling is less than -1.5, the oscillation of the
$T_{vv}$ component allows the apparent horizon to shrink. This allows a
combination that violates weak cosmic censorship. Finally, we discuss the
implications of the violation of the null energy condition and weak cosmic
censorship.
