  Boundary conditions and the corresponding states of a quantum field theory
depend on how the horizons are taken into account. There is ambiguity as to
which method is appropriate because different ways of incorporating the
horizons lead to different results. We propose that a natural way of including
the horizons is to first consider the Kruskal extension and then define the
quantum field theory on the Euclidean section. Boundary conditions emerge
naturally as consistency conditions of the Kruskal extension. We carry out the
proposal for the explicit case of the Schwarzschild-de Sitter manifold with two
horizons. The required period $\beta$ is the interesting condition that it is
the lowest common multiple of $2\pi$ divided by the surface gravity of both
horizons. Restricting the ratio of the surface gravity of the horizons to
rational numbers yields finite $\beta$. The example also highlights some of the
difficulties of the off-shell approach with conical singularities in the
multihorizon scenario; and serves to illustrate the much richer interplay that
can occur among horizons, quantum field theory and topology when the
cosmological constant is not neglected in black hole processes.
