We consider the covariant Klein-Gordon equation (□ g g+ m 2) φ= 0 of mass m≥ 0 on the
exterior Schwarzschild spacetime of mass M. We introduce and study a set of outer and
inner wave operators Ω 0±, Ω 1±(constructed in detail elsewhere) describing the asymptotic
behavior of classical solutions—Ω 0±for large distances and Ω 1±near the Schwarzschild
radius—as t→±∞. We re-interpret Ω 1±on the Kruskal spacetime as solving a characteristic
initial value problem for data on the future/past right horizon H±. As a by-product, we prove …

An alternate treatment of the results of paper I is given. As in that paper, the Unruh boundary
condition is formulated, the Unruh vacuum is defined as a state satisfying this boundary
condition, and the thermal character of the state is exhibited. The present work differs in that
it uses the double-wedge region of the Kruskal manifold and defines and uses a precise
notion of distinguished modes.