  We analyse the smooth and sharp creation of a pointlike source for a
quantised massless scalar field in $(3+1)$-dimensional Minkowski spacetime, as
a model for the breakdown of correlations that has been proposed to occur at
the horizon of an evaporating black hole. The creation is implemented by a
time-dependent self-adjointness parameter at the excised spatial origin. In a
smooth creation, the renormalised energy density $\langle T_{00} \rangle$ is
well defined away from the source, but it is unbounded both above and below:
the outgoing pulse contains an infinite negative energy, while a cloud of
infinite positive energy lingers near the fully-formed source. In the sharp
creation limit, $\langle T_{00} \rangle$ diverges everywhere in the timelike
future of the creation event, and so does the response of an Unruh-DeWitt
detector that operates in the timelike future of the creation event. The source
creation is significantly more singular than the corresponding process in $1+1$
dimensions, analysed previously, and it may be sufficiently singular to break
quantum correlations as proposed in a black hole spacetime.
