  We construct the general 2+1 dimensional asymptotically AdS_3 solution dual
to a stationary 1+1 CFT state on a black hole background. These states involve
heat transport by the CFT between the 1+1 black hole and infinity (or between
two 1+1 black holes), and so describe the AdS dual of CFT Hawking radiation.
Although the CFT stress tensor is typically singular at the past horizon of the
1+1 black hole, the bulk 2+1-dimensional solutions are everywhere smooth, and
in fact are diffeomorphic to AdS_3. In particular, we find that Unruh states of
the CFT on any finite-temperature 1+1 black hole background are described by
extreme horizons in the bulk.
