INEXTENDIBLE SCHWARZSCHILD BLACK-HOLE WITH A SINGLE EXTERIOR - HOW THERMAL IS THE HAWKING RADIATION - ART. NO. 024007

Several approaches to Hawking radiation on Schwarzschild spacetime rel y 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 RP3 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 Hartle-Hawking-like vacuum \0(G)], whic h can be characterized alternatively by the positive frequency propert ies along the horizons or by the complex analytic properties of the Fe ynman propagator, turns out to contain exterior region Boulware modes in correlated pairs, and any operator in the exterior that only couple s to one member of each correlated Boulware pair has thermal expectati on values in the usual Hawking temperature. Generic operators in the e xterior do not have this special form; however, we use a Bogoliubov tr ansformation, a particle detector analysis, and a particle emission-ab sorption analysis that invokes the analytic properties of the Feynman propagator, to argue that \0(G)] appears as a thermal bath with the st andard Hawking temperature to any exterior observer at asymptotically early and late Schwarzschild times. A (naive) saddle-point estimate fo r the path-integral-approach partition function yields for the geon on ly half of the Bekenstein-Hawking entropy of a Schwarzschild black hol e with the same ADM mass: possible implications of this result for the validity of path-integral methods or for the statistical interpretati on of black-hole entropy are discussed. Analogous results hold for a R indler observer in a flat spacetime whose global properties mimic thos e of the geon. [S0556-2821(98)06614-4].