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• W2003222039 abstract "We consider the covariant Klein-Gordon equation (□gg+m2) 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 Ω0±, Ω1± (constructed in detail elsewhere) describing the asymptotic behavior of classical solutions—Ω0± for large distances and Ω1± near the Schwarzschild radius—as t→±∞. We re-interpret Ω1± 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 (since we require it here) a stronger result than previously known concerning the stability of the Schwarzschild black hole against linearized (scalar) perturbations. Using Ω0+, Ω1+ we construct in and out and horizon fields for the corresponding quantum problem. We give a construction for the Hartle-Hawking state ωH and prove that it coincides on the in and out fields with a state of exact thermal equilibrium in Minkowski space, while its two-point function on the (right) horizons H± is given (independently of m) by ωH[(δUø̂)(U1,ξ1)(δUø̂)(U2,ξ2)] = (−δ(ξ1,ξ2)/16φM2)(U1−U2−iϵ)−2 (U1, U2ϵ (−∞, 0), ξ1, ξ2 ϵ S2) on H− and by a similar formula (with U→V, (−∞, 0) → (0, ∞), etc.) on H+. We also construct the Unruh state ωU as a product state, equal to the Minkowski vacuum on the in field, and with two-point function on H− equal to that given above for ωH. We prove that the restriction of this ωU to the out field coincides with a particular state of thermal radiation in Minkowski space. A special feature of our treatment is that we relate the horizon behavior of φ̂ with the light-cone behavior of a massless free scalar field φ̂1 in a two-dimensional flat spacetime: δ2ø̂1δT2−δ2ø̂1δX2 = 0. In particular, using our classical characteristic-intial-value-problem results, we explain why the above expression for the two-point function of ∂Uφ̂ on H is identical (modulo the trivial role played by S2 and up to a scale factor of 2M) with the well-known two-point function for ∂Uφ̂1 (U=T−X) on the null line T + X = 0." @default.
• W2003222039 created "2016-06-24" @default.
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• W2003222039 date "1987-05-01" @default.
• W2003222039 modified "2023-10-17" @default.
• W2003222039 title "Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric I" @default.
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• W2003222039 doi "https://doi.org/10.1016/0003-4916(87)90214-4" @default.
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