  I consider the problem of reconciling "tunneling" approaches to black-hole
radiation with the treatment by quantum field theory in curved space-time. It
is not possible to do this completely, but using what appears to be the most
direct and natural correspondence, the simplest case of such an approach does
not describe a tunneling process but rather a WKB approximation to a two-point
function. What it computes is a sort of rescaled Unruh temperature associated
with world-lines tracing Killing trajectories near the horizon. This
temperature is numerically equal to the Hawking temperature, but at this point
no argument is known which identifies it with the Hawking effect; indeed, the
same temperature can exist when no curvature is present.
