×
Bachelot, Alain

Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric. (English) Zbl 0809.35141

Ann. Inst. Henri Poincaré, Phys. Théor. 61, No. 4, 411-441 (1994).
Summary: We prove the strong asymptotic completeness of the wave operators, classic at the horizon and Dollard-modified at infinity, describing the scattering of a massive Klein-Gordon field by a Schwarzschild black hole. The scattering operator is unitarily implementable in the Fock space of free fields.

Cited in 20 Documents

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
85A15 Galactic and stellar structure

Keywords:

wave operators; scattering of a massive Klein-Gordon field by a Schwarzschild blackhole; scattering operator
PDF BibTeX XML Cite
\textit{A. Bachelot}, Ann. Inst. Henri Poincaré, Phys. Théor. 61, No. 4, 411--441 (1994; Zbl 0809.35141)
Full Text: Numdam EuDML

References:

[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 . Article | MR 345551 | Zbl 0219.47011 · Zbl 0219.47011
[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 1122656 | Zbl 0743.53037 · Zbl 0743.53037
[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 0823.35162 · Zbl 0823.35162
[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 1244181 | Zbl 0793.53094 · Zbl 0793.53094
[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 1222970 | Zbl 0776.35052 · Zbl 0776.35052
[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 1135574 | Zbl 0732.46040 · Zbl 0732.46040
[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 701057 | Zbl 0516.60069 · Zbl 0516.60069
[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 432051 | Zbl 0344.47007 · Zbl 0344.47007
[9] J. Dimock , Scattering for the Wave Equation on the Schwarzschild Metric , Gen. Rel. Grav. Vol. 17 , 1985 , pp. 353 - 369 . MR 788801 | Zbl 0618.35088 · Zbl 0618.35088
[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 821837 | Zbl 0659.53054 · Zbl 0659.53054
[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 887979 | Zbl 0628.53080 · Zbl 0628.53080
[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 857397 | Zbl 0608.53065 · Zbl 0608.53065
[13] T. Kato , Perturbation Theory for Linear Operators , Springer-Verlag , New York , 1966 . MR 203473 | Zbl 0148.12601 · Zbl 0148.12601
[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 543906
[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 . Article | MR 796162 | Zbl 0578.46062 · Zbl 0578.46062
[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 . Article | MR 634802 | Zbl 0356.47006 · Zbl 0356.47006
[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 . Article | MR 634803 | Zbl 0388.35055 · Zbl 0388.35055
[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 . · Zbl 0308.47002
[20] E.M. Stein and G. Weiss , Introduction to Fourier Analysis on Euclidean Spaces , Princeton University Press , 1971 . MR 304972 | Zbl 0232.42007 · Zbl 0232.42007
[21] M. Weinless , Existence and Uniqueness of the Vaccum for Linear Quantized Fields , J. Funct. Anal. , T. 4 , 1969 , pp. 350 - 379 . MR 253687 | Zbl 0205.57504 · Zbl 0205.57504
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.