Local scalar QFT (in Weyl algebraic approach) is constructed on degenerate
semi-Riemannian manifolds corresponding to Killing horizons in spacetime.
Covariance properties of the C∗-algebra of observables with respect to the
conformal group PSL(2,\bR) are studied.It is shown that, in addition to the
state studied by Guido, Longo, Roberts and Verch for bifurcated Killing
horizons, which is conformally invariant and KMS at Hawking temperature with
respect to the Killing flow and defines a conformal net of von Neumann
algebras, there is a further wide class of algebraic (coherent) states
representing spontaneous breaking of PSL(2,\bR) symmetry. This class is
labeled by functions in a suitable Hilbert space and their GNS representations
enjoy remarkable properties. The states are non equivalent extremal KMS states
at Hawking temperature with respect to the residual one-parameter subgroup of
PSL(2,\bR) associated with the Killing flow. The KMS property is valid for
the two local sub algebras of observables uniquely determined by covariance and
invariance under the residual symmetry unitarily represented. These algebras
rely on the physical region of the manifold corresponding to a Killing horizon
cleaned up by removing the unphysical points at infinity (necessary to describe
the whole PSL(2,\bR) action).Each of the found states can be interpreted as a
different thermodynamic phase, containing Bose-Einstein condensate,for the
considered quantum field. It is finally suggested that the found states could
describe different black holes.Comment: 36 pages, 1 figure. Formula of condensate energy density modified.
Accepted for pubblication in Journal of Mathematical Physic