  The classic singularity theorems of General Relativity rely on energy
conditions that can be violated in semiclassical gravity. Here, we provide
motivation for an energy condition obeyed by semiclassical gravity: the smeared
null energy condition (SNEC), a proposed bound on the weighted average of the
null energy along a finite portion of a null geodesic. We then prove a
semiclassical singularity theorem using SNEC as an assumption. This theorem
extends the Penrose theorem to semiclassical gravity. We also apply our bound
to evaporating black holes and the traversable wormhole of
Maldacena-Milekhin-Popov, and comment on the relationship of our results to
other proposed semiclassical singularity theorems.
