  The classical singularity theorems of General Relativity rely on energy
conditions that are easily violated by quantum fields. Here, we provide
motivation for an energy condition obeyed in 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. Using SNEC as an
assumption we proceed to prove a singularity theorem. This theorem extends the
Penrose singularity theorem to semiclassical gravity and has interesting
applications to evaporating black holes.
