Schwarzschild black hole with a single exterior : How thermal is the Hawking radiation ?

Several approaches to Hawking radiation on the Schwarzschild spacetime rely in some way or another on the fact that the Kruskal manifold has two causally disconnected exterior regions. To assess the physical input implied by the presence of the second exterior region, we investigate the Hawking(-Unruh) effect for a real scalar field on the RP geon: an inextendible, globally hyperbolic, space and time orientable eternal black hole spacetime that is locally isometric to Kruskal but contains only one exterior region. The HartleHawking-like vacuum |0G〉, which can be characterized alternatively by the positive frequency properties along the horizons or by the complex analytic properties of the Feynman propagator, turns out to contain exterior region Boulware modes in correlated pairs, and any operator in the exterior that only couples to one member of each correlated Boulware pair has thermal expectation values in the usual Hawking temperature. Generic operators in the exterior do not have this special form; however, we use a Bogoliubov transformation, a particle detector analysis, and a particle emission-absorption analysis that invokes the analytic properties of the Feynman propagator, to ∗Electronic address: [email protected] †Present address. ‡Electronic address: [email protected]