  We study string theory on the extended spacetime of the BTZ black hole, as
described by an orbifold of the SL(2,R) WZW model. The full spacetime has an
infinite number of disconnected boundary components, each corresponding to a
dual CFT. We discuss the computation of bulk and boundary correlation functions
for operators inserted on different components. String theory correlation
functions are obtained by analytic continuation from an orbifold of the
SL(2,C)/SU(2) coset model. This yields two-point functions for general
operators, including those describing strings that wind around the horizon of
the black hole.
