How thermal is Hawking radiation on the RP geon?

We investigate the Hawking(-Unruh) effect for a real scalar field on the eternal black hole spacetime known as the RP geon. The Hartle-Hawking-like vacuum |0G〉 turns out to contain Boulware modes in correlated pairs, and operators that only couple to one member of each pair have thermal expectation values at the usual Hawking temperature. As both members of each correlated Boulware pair reside in the single exterior Schwarzschild region, not all operators with support in the exterior region have thermal expectation values; 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 argue that |0G〉 appears as a thermal bath with the standard Hawking temperature at asymptotically early and late exterior Schwarzschild times. A (naive) saddle-point estimate for the path-integral-approach partition function yields for the geon only half of the Bekenstein-Hawking entropy of a Schwarzschild black hole with the same ADM mass. Analogous results hold for a Rindler observer in a flat spacetime ∗Electronic address: [email protected] †Present address. ‡Electronic address: [email protected]