  Recent developments suggest that the near-region of rotating black holes
behaves like a CFT. To understand this better, I propose to study quantum
fields in this region. An instructive approach for this might be to put a large
black hole in AdS and to think of the entire geometry as a toy model for the
``near-region". Quantum field theory on rotating black holes in AdS can be
well-defined (unlike in flat space), if fields are quantized in the
co-rotating-with-the-horizon frame. First, some generalities of constructing
Hartle-Hawking Green functions in this approach are discussed. Then as a
specific example where the details are easy to handle, I turn to 2+1 dimensions
(BTZ), write down the Green functions explicitly starting with the co-rotating
frame, and observe some structural similarities they have with the Kerr-CFT
scattering amplitudes. Finally, in BTZ, there is also an alternate construction
for the Green functions: we can start from the covering AdS_3 space and use the
method of images. Using a 19th century integral formula, I show the equality
between the boundary correlators arising via the two constructions.
