We construct a state in the Schwarzschild-de Sitter spacetime which is
invariant under the action of its group of symmetries. Our state is not defined
in the whole Kruskal extension of this spacetime, but rather in a subset of the
maximally extended conformal diagram. The construction is based on a careful
use of the bulk-to-boundary technique. We will show that our state is Hadamard
and that it is not a KMS state, differently from the case of states constructed
in spacetimes containing only one event horizon.Comment: More emphasis put on the result. 41 pages. Uses natbib and iopart.
This version is going to be published in Classical and Quantum Gravity. PACS
numbers: 04.62.+v,04.70.Dy,03.65.Fd. arXiv admin note: text overlap with
arXiv:0907.1034 by other author
