Dimock, J. Scattering for the wave equation on the Schwarzschild metric. (English) Zbl 0618.35088 Gen. Relativ. Gravitation 17, 353-369 (1985). The scattering problem for the massless scalar field in Schwarzschild’s space-time is studied at length. Special (tortoise) coordinates are used, in which the horizon is placed at infinity. This implies that the wave operator has to be constructed in two distinct asymptotic domains, namely the horizon and the Minkowski regions of space-time. The existence of the wave operator follows from the adaption of the existence theorem for a general class of asymptotically flat space-times. Reviewer: M.Maia Cited in 29 Documents MSC: 35P25 Scattering theory for PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory Keywords:scattering; massless scalar field; Schwarzschild’s space-time; wave operator; horizon; Minkowski regions of space-time × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Dimock, J., and Kay, B. Scattering for scalar fields on Coulomb potentials and Schwarzschild metrics (to appear). · Zbl 0659.53054 [2] Dimock, J., and Kay, B. Scattering for scalar quantum fields on black hole metrics (to appear). · Zbl 0591.35080 [3] Dimock, J., and Kay, B. (1982).,Ann. Inst. Henri Poincaré,37, 93-114. [4] Kato, T. (1970).J. Functional Analysis,1, 342-369. · Zbl 0171.12303 · doi:10.1016/0022-1236(67)90019-5 [5] Reed, M., and B. Simon, (1977).Math. Z.,155, 163-180. · doi:10.1007/BF01214216 [6] Reed, M., and Simon, B. (1979).Methods of Modern Mathematical Physics, Vol. III (Academic Press, New York). · Zbl 0405.47007 [7] Kato, T. (1966).Perturbation Theory for Linear Operators (Springer-Verlag, New York). · Zbl 0148.12601 [8] Reed, M., and Simon, B. (1975).Methods of Modern Mathematical Physics, Vol. II (Academic Press, New York). · Zbl 0308.47002 [9] Reed, M., and Simon, B. (1978).Methods of Modern Mathematical Physics, Vol. IV (Academic Press, New York). · Zbl 0401.47001 [10] Beig, R. (1982).Acta Phys. Austr.,54, 129. [11] Davies, E. B., and Simon, B. (1978).Commun. Math. Phys.,63, 277-301. · Zbl 0393.34015 · doi:10.1007/BF01196937 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.