  The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions
all admit freely acting discrete involutions which commute with the continuous
symmetries of the spacetimes. Intuitively, these involutions correspond to the
antipodal map of the corresponding spacetimes. In analogy with the ordinary de
Sitter example, this allows us to construct new vacua by performing a
Mottola-Allen transform on the modes associated with the Hartle-Hawking, or
Euclidean, vacuum. These vacua are the `alpha'-vacua for these black holes. The
causal structure of a typical black hole may ameliorate certain difficulties
which are encountered in the case of de Sitter alpha-vacua. For
Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes
operators of the two boundary CFT's provides a construction of the dual CFT
alpha-states. Finally, we analyze the thermal properties of these vacua.
