  Considerable interest has recently been expressed regarding the issue of
whether or not quantum field theory on a fixed but curved background spacetime
satisfies the averaged null energy condition (ANEC). A comment by Wald and
Yurtsever [Phys. Rev. D43, 403 (1991)] indicates that in general the answer is
no. In this note I explore this issue in more detail, and succeed in
characterizing a broad class of spacetimes in which the ANEC is guaranteed to
be violated. Finally, I add some comments regarding ANEC violation in
Schwarzschild spacetime.
