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Abstract
We consider black holes in an "unsuitable box": a finite cavity coupled to a thermal
reservoir at a temperature different than the black hole's Hawking temperature. These
black holes are described by metrics that are continuous but not differentiable due
to a conical singularity at the horizon. We include them in the Euclidean path integral
sum over configurations, and analyze the effect this has on black hole thermodynamics
in the canonical ensemble. Black holes with a small deficit (or surplus) angle may
have a smaller internal energy or larger density of states than the nearby smooth
black hole, but they always have a larger free energy. Furthermore, we find that the
ground state of the ensemble never possesses a conical singularity. When the ground
state is a black hole, the contributions to the canonical partition function from
configurations with a conical singularity are comparable to the contributions from
smooth fluctuations of the fields around the black hole background. Our focus is on
highly symmetric black holes that can be treated as solutions of two-dimensional dilaton
gravity models: examples include Schwarzschild, asymptotically Anti-de Sitter, and
stringy black holes.