  We investigate gravitational collapse of a $(3+1)$-dimensional BTZ black
string in AdS space in the context of both classical and quantum mechanics.
This is done by first deriving the conserved mass per unit length of the
cylindrically symmetric domain wall, which is taken as the classical
Hamiltonian of the black string. In the quantum mechanical context, we take
primary interest in the behavior of the collapse near the horizon and near the
origin (classical singularity) from the point of view of an infalling observer.
In the absence of radiation, quantum effects near the horizon do not change the
classical conclusions for an infalling observer, meaning that the horizon is
not an obstacle for him/her. The most interesting quantum mechanical effect
comes in when investigating near the origin. First, quantum effects are able to
remove the classical singularity at the origin, since the wave function is
non-singular at the origin. Second, the Schr\"odinger equation describing the
behavior near the origin displays non-local effects, which depend on the energy
density of the domain wall. This is manifest in that derivatives of the
wavefunction at one point are related to the value of the wavefunction at some
other distant point.
