Les résonances d'un trou noir de Schwarzschild
Bachelot, Alain ; Motet-Bachelot, Agnès
Annales de l'I.H.P. Physique théorique, Tome 59 (1993), p. 3-68 / Harvested from Numdam
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@article{AIHPA_1993__59_1_3_0,
     author = {Bachelot, Alain and Motet-Bachelot, Agn\`es},
     title = {Les r\'esonances d'un trou noir de Schwarzschild},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {59},
     year = {1993},
     pages = {3-68},
     mrnumber = {1244181},
     zbl = {0793.53094},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPA_1993__59_1_3_0}
}

Bachelot, Alain; Motet-Bachelot, Agnès. Les résonances d'un trou noir de Schwarzschild. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) pp. 3-68. http://gdmltest.u-ga.fr/item/AIHPA_1993__59_1_3_0/

[1] V. De Alfaro et T. Regge, Potential Scattering, North Holland, Amsterdam, 1965. | MR 191316 | Zbl 0141.23202

[2] A. Bachelot, Gravitational Scattering of electromagnetic field by Schwarzschild Black-Hole, Ann. Inst. H. Poincaré, Phys. Théor., vol. 54, n° 3, 1991, p. 261-320. | Numdam | MR 1122656 | Zbl 0743.53037

[3] R.P. Boas, Entire Functions, Academic Press, New York, 1954. | MR 68627 | Zbl 0058.30201

[4] N.G. De Bruijn, Asymptotic Methods in Analysis, Dover, New York, 1981. | MR 671583 | Zbl 0556.41021

[5] S. Chandrasekar, The mathematical theory of black-holes, Oxford University Press, New York, 1983. | MR 700826 | Zbl 0511.53076

[6] S. Chandrasekar, On algebraically special perturbations of black holes, Proc. R. Soc. Lond. A, vol. 392, 1984, p. 1-13. | MR 738924

[7] S. Chandrasekar, S. Detweiler, The quasi-normal modes of the Schwarzschild blackhole, Proc. R. Soc. Lond. A, vol. 344, 1975, p. 441-452.

[8] T. Damour, Black-Hole eddy currents, Phys. Rev. D., vol. 18, 10, 1978, p. 3598-3604.

[9] T. Damour, Thèse de Doctorat d'État, Université Pierre-et-Marie-Curie, Paris, 1979.

[10] T. Damour, in Proceedings of the Second Marcel Grossman Meeting on General Relativity, Ruffini Edt, North-Holland, Amsterdam, 1982. | MR 678971

[11] P. Deift et E. Trubowitz, Inverse Scattering on the Line, Comm. Pure Appl. Math., vol. 32, 1979, p. 121-251. | MR 512420 | Zbl 0388.34005

[12] J. Dimock, Scattering for the wave equation on the Schwarzschild metric, Gen. Rel. Grav., vol. 17, 4, 1985, p. 353-369. | MR 788801 | Zbl 0618.35088

[13] B. Engquist et A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math., vol. 32, 1979, p. 313-357. | MR 517938 | Zbl 0387.76070

[14] V. Ferrari, B. Mashhoon, New approach to the quasinormal modes of a black-hole, Phys. Rev. D, vol. 30, 2, 1984, p. 295-304. | MR 750250

[15] J.W. Guinn, Y. Kojima et B.F. Schutz, High-overtone normal modes of Schwarzschild black-holes, Class. Quantum Grav., vol. 7, 1990, p. 47-53. | MR 1042874

[16] J.B. Hartle et D.C. Wilkins, Analytic Properties of the Teukolsky Equation, Comm. Math. Phys., vol. 38, 1974, p. 47-63. | MR 351359

[17] S. Iyer, Black-hole normal modes: a WKB approach II; Schwarzschild black holes, Phys. Rev. D, vol. 35, 12, 1987, p. 3632-3636.

[18] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966. | MR 203473 | Zbl 0148.12601

[19] K.D. Kokkotas, Normal modes of the Kerr black-hole, Class. Quantum Grav., vol. 8, 1991, p. 2217-2224. | MR 1141038 | Zbl 0729.83501

[20] P. Lax et R. Phillips, Scattering Theory, Academic Press, New York, nouvelle édition 1989. | MR 1037774 | Zbl 0697.35004

[21] E. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D, vol. 34, 2, 1986, p. 384-408. | MR 848080

[22] E. Leaver, An analytic representation for the quasi-normal modes of Kerr black-holes, Proc. R. Soc. Lond. A, vol. 402, 1985, p. 285-298. | MR 828221

[23] D.A. Macdonald, R.H. Price, K.S. Thorne, Black-Holes: The Membrane Paradigm, Yale University Press, New Haven, London, 1986. | MR 912528

[24] G. Majda, W. Strauss et M. Wei, Numerical Computation of the Scattering Frequencies for Acoustic Wave Equations, Comput. Phys., vol. 75, 2, 1988, p. 345-358. | Zbl 0643.65080

[25] B. Majumda et N. Panchapakesan, Schwarzschild black-hole normal modes using the Hill determinant, Phys. Rev. D., vol. 40, 1989, p. 2568-2571. | MR 1019504

[26] E.K. Miller, R. Mittra, A.J. Poggio, M.L. Van Blaricum, Evaluation of a Processing Technique for Transient Data, IEEE Trans. Antennas Propagat., vol. 36, 1, 1978, p. 165-173.

[27] R. Mittra, M.L. Van Blaricum, A Technique for Extracting the Poles and Residues of a System Directly from Its Transient Response, IEEE Trans. Antennas Propagat., vol. 23, 6, 1975, p. 777-781.

[28] R.G. Newton, Scattering Theory of Waves and Particles, McGraw-Hill, New York, 1966. | MR 221823

[29] H.P. Nollert, Doktorarbeit, Universitât Tübingen, 1991.

[30] H.P. Nollert, B.G. Schmidt, Quasi-Normal Modes of Schwarzschild Black-Holes-Defined and Calculated via Laplace Transformtion, preprint, 1992. | MR 1157096

[31] R. Phillips, Scattering Theory for the Wave Equation with a Short Range Perturbation II, Indiana Univ. Math. J., vol. 33, 6, 1984, p. 831-846. | MR 763944 | Zbl 0526.35066

[32] R.H. Price, Y. Sun, Excitation of quasinormal ringing of a Schwarzschild black-hole, Phys. Rev. D, vol. 38, 4, 1988, p. 1040-1052. | MR 962227

[33] R. Prony, Essai expérimental et analytique sur les lois de la dilatabilité de fluides élastiques et sur celles de la force expansive de la vapeur de l'alcool à différentes températures, J. de l'École Polytechnique, vol. 1, cahier 2, 1795, p. 24-76.

[34] M. Reed et B. Simon, Methods ofmodern mathematical physics, vol. III, 1979, Academic Press. | Zbl 0405.47007

[35] M. Reed et B. Simon, Methods of modern mathematical physics, vol. IV, 1978, Academic Press. | Zbl 0401.47001

[36] T. Regge, Analytic Properties of the Scattering Matrix, Il Novo Cimento, vol. 8, 5, 1958, p. 671-679. | MR 95702 | Zbl 0080.41903

[37] M. Schechter, Operator Methods in Quantum Mechanics, North Holland, New York, Oxford, 1981. | MR 597895 | Zbl 0456.47012

[38] B. Schmidt, Communication privée, I.H.E.S., mars 1990.

[39] M. Wei, Numerical Computation of Scattering Frequencies, Ph. D. Thesis, Dept. of Applied Math., Brown Univ., Providence, RI, 1986.

[40] M. Zworski, Distribution of Poles for Scattering on the Real Line, J. Funct. Anal., vol. 73, 1987, p. 277-296. | MR 899652 | Zbl 0662.34033