  We study the time evolution of the Misner-Sharp mass and the apparent horizon
for gravitational collapse of a massless scalar field in the $AdS_{5}$
space-time for both cases of narrow and broad waves by numerically solving the
Einstein's equations coupled to a massless scalar field. This is done by
relying on the full dynamics of the collapse including the concept of the
dynamical horizon. It turns out that the Misner-Sharp mass is everywhere
constant except for a rapid change across a thin shell defined by the density
profile of the collapsing wave. By studying the evolution of the apparent
horizon, indicating the formation of a black hole at different times we see how
asymptotically an event horizon forms. The dependence of the thermalization
time on the radius of the initial black hole event horizon is also studied.
