  Using the eternal BTZ black hole as a concrete example, we show how spacelike
singularities and horizons can be described in terms of AdS/CFT amplitudes. Our
approach is based on analytically continuing amplitudes defined in Euclidean
signature. This procedure yields finite Lorentzian amplitudes. The naive
divergences associated with the Milne type singularity of BTZ are regulated by
an $i\epsilon$ prescription inherent in the analytic continuation and a
cancellation between future and past singularities.
  The boundary description corresponds to a tensor product of two CFTs in an
entangled state, as in previous work. We give two bulk descriptions
corresponding to two different analytic continuations. In the first, only
regions outside the horizon appear explicitly, and so amplitudes are manifestly
finite. In the second, regions behind the horizon and on both sides of the
singularity appear, thus yielding finite amplitudes for virtual particles
propagating through the black hole singularity. This equivalence between
descriptions only outside and both inside and outside the horizon is
reminiscent of the ideas of black hole complementarity.
