  Black hole microstates and their approximate thermodynamic properties can be
studied using heavy-light correlation functions in AdS/CFT. Universal features
of these correlators can be extracted from the Virasoro conformal blocks in
CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite
central charge c, the Virasoro vacuum block provides an avatar of the black
hole information paradox in the form of periodic Euclidean-time singularities
that must be resolved at finite c.
  We compute Virasoro blocks in the heavy-light, large c limit, extending our
previous results by determining perturbative 1/c corrections. We obtain
explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$
and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide
integral formulas for general Virasoro blocks. We comment on the interpretation
of our results for thermodynamics, discussing how monodromies in Euclidean time
can arise from AdS calculations using `geodesic Witten diagrams'. We expect
that only non-perturbative corrections in 1/c can resolve the singularities
associated with the information paradox.
