  It is generally agreed that black hole formation in gravity corresponds to
thermalization in the dual CFT. It is sometimes argued that if the CFT
evolution shows evidence of large redshift in gravity, then we have seen black
hole formation in the CFT. We argue that this is not the case: a clock falling
towards the horizon increases its redshift but remains intact as a clock; thus
it is not `thermalized'. Instead, thermalization should correspond to a new
phase after the phase of large redshift, where the infalling object turns into
fuzzballs on reaching within planck distance of the horizon. We compute simple
examples of the scattering vertex in the D1D5 CFT which, after many iterations,
would lead to thermalization. An initial state made of two left-moving and two
right-moving excitations corresponds, in gravity, to two gravitons heading
towards each other. The thermalization vertex in the CFT breaks these
excitations into multiple excitations on the left and right sides; we compute
the amplitudes for several of these processes. We find secular terms that grow
as $t^2$ instead of oscillating with $t$; we conjecture that this may be a
feature of processes leading to thermalization.
