  We discuss quantum properties of the single-exterior, geon-type black (and
white) holes that are obtained from the Kruskal spacetime and the spinless
Banados-Teitelboim-Zanelli hole via a quotient construction that identifies the
two exterior regions. For the four-dimensional geon, the Hartle-Hawking type
state of a massless scalar field is thermal in a limited sense, but there is a
discrepancy between Lorentzian and Riemannian derivations of the geon entropy.
For the three-dimensional geon, the state induced for a free conformal scalar
field on the conformal boundary is similarly thermal in a limited sense, and
the correlations in this state provide support for the holographic hypothesis
in the context of asymptotically anti-de Sitter black holes in string theory.
