Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric
Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 4, pp. 411-441. 
@article{AIHPA_1994__61_4_411_0,
     author = {Bachelot, Alain},
     title = {Asymptotic completeness for the {Klein-Gordon} equation on the {Schwarzschild} metric},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {411--441},
     publisher = {Gauthier-Villars},
     volume = {61},
     number = {4},
     year = {1994},
     mrnumber = {1311537},
     zbl = {0809.35141},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1994__61_4_411_0/}
}
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Bachelot, Alain. Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 4, pp. 411-441. http://archive.numdam.org/item/AIHPA_1994__61_4_411_0/

[1] J. Aguilar and J.M. Combes, A Class of Analytic Perturbations for one Body Schrödinger Hamiltonians, Comm. Math. Phys. Vol. 22, 1971, pp. 269-279. | MR | Zbl

[2] A. Bachelot, Gravitational Scattering of Electromagnetic Field by Schwarzschild Black-Hole, Ann. I.H.P.. Physique théorique, Vol. 54, 1991, pp. 261-320. | Numdam | MR | Zbl

[3] A. Bachelot, Scattering of Electromagnetic Field by De Sitter-Schwarzschild Black-Hole, in Non Linear Hyperbolic Equations and Field Theory, Research Notes in Math, Vol. 253, 1992, Pitman. | Zbl

[4] A. Bachelot and A. Motet-Bachelot, Les résonances d'un trou noir de Schwarschild, Ann I.H.P. Physique théorique, Vol. 59, 1993, pp. 3-68. | Numdam | MR | Zbl

[5] A. Bachelot and J.-P. Nicolas, Équation non linéaire de Klein-Gordon dans des métriques de type Schwarzschild, C.R. Acad. Sci. Paris, T. 316, Série I, 1993, pp. 1047-1050. | MR | Zbl

[6] N.N. Bogolubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General Principles of Quantum Field Theory, Kluwer Academic Publischers, Dordrecht, 1990. | MR | Zbl

[7] R. Carmona, One Dimensional Schrödinger Operators with Random or Deterministic Potentials: New Spectral Types, J. Func. Anal., Vol. 51, 1983, pp. 229-258. | MR | Zbl

[8] P. Deift and B. Simon, On the Decoupling of Finite Singularities from the Question of Asymptotic Completeness in two Body Quantum System, J. Func. Anal., Vol. 23, 1976, pp. 218-238. | MR | Zbl

[9] J. Dimock, Scattering for the Wave Equation on the Schwarzschild Metric, Gen. Rel. Grav. Vol. 17, 1985, pp. 353-369. | MR | Zbl

[10] J. Dimock and B.S. Kay, Scattering for Massive Scalar Fields on Coulomb Potentials and Schwarzschild metrics, Class. Quantum Grav., Vol. 3, 1986, pp. 71-80. | MR | Zbl

[11] J. Dimock and B.S. Kay, Classical and Quantum Scattering Theory for Linear scalar fields on the Schwarzschild Metric I, Ann. Phys., Vol. 175, 1987, pp. 366-426. | MR | Zbl

[12] J. Dimock and B.S. Kay, Classical and Quantum Scattering Theory for Linear Scalar Fields on the Schwarzschild Metric II, J. Math. Phys., Vol. 27, 1986, pp. 2520-2525. | MR | Zbl

[ 13] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966. | MR | Zbl

[14] B.S. Kay, A Uniqueness result in the Segal-Weinless Approach to Linear Bose Fileds, J. Math. Phys., Vol. 20, 1979, pp. 1712-1713. | MR

[15] B.S. Kay, The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes, Commun. Math. Phys., Vol. 100, 1985, pp. 57-81. | MR | Zbl

[16] H. Kitada, Scattering theory for Schrödinger Operators with Long Range Potentials, I, Abstract Theory, J. Math., Soc. Japan, Vol. 29, 1977, pp. 665-691. | MR | Zbl

[17] H. Kitada, Scattering Theory for Schrödinger Operators with Long Range potentials, II, Spectral and Scattering Theory, J. Math. Soc. Japan, Vol. 30, 1978, pp. 603-632. | MR | Zbl

[18] J.P. Nicolas, Équation non linéaire de Klein-Gordon et système de Dirac dans des métriques de type Schwarzschild, Thèse de Doctorat, Université Bordaux-I, 1994.

[19] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, III, 1975, 1978, Academic Press.

[20] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. | MR | Zbl

[21] M. Weinless, Existence and Uniqueness of the Vaccum for Linear Quantized Fields, J. Funct. Anal., T. 4, 1969, pp. 350-379. | MR | Zbl