Klein Paradox and Superradiance for the charged Klein-Gordon Field
Bachelot, Alain1
1 Université Bordeaux-1, Institut de Mathématiques, UMR CNRS 5466, F-33405 Talence Cedex
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 22, 11 p.
Bachelot, Alain 1

1 Université Bordeaux-1, Institut de Mathématiques, UMR CNRS 5466, F-33405 Talence Cedex 
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     title = {Klein {Paradox} and {Superradiance} for the charged {Klein-Gordon} {Field}},
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Bachelot, Alain. Klein Paradox and Superradiance for the charged Klein-Gordon Field. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 22, 11 p. http://archive.numdam.org/item/SEDP_2003-2004____A22_0/

[1] A. Bachelot. Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric. Ann. Inst. Henri Poincaré - Physique théorique, 61 (4) : 411–441, 1994. | Numdam | MR | Zbl

[2] A. Bachelot. Global properties of the wave equation on non globally hyperbolic manifolds. J. Math. Pures Appl., 81 : 35-65, 2002. | MR | Zbl

[3] A. Bachelot. Superradiance and Scattering of the charged Klein-Gordon Field by a Steplike Electrostatic Potential. J. Math. Pures Appl., to appear, 2004. | Zbl

[4] E. Bairamov, Ö. Çakar, A. M. Krall. An Eigenfunction Expansion for a Quadratic Pencil of a Schrödinger Operator with Spectral Singularities. J. Diff. Eqs., 151 : 268–289, 1999. | MR | Zbl

[5] A. Cohen, T. Kappeler. Scattering and Inverse Scattering for Steplike Potentials in the Schrödinger Equation. Indiana Univ. Math. J., 34 (1) : 127–180, 1985. | MR | Zbl

[6] E.B. Davies, B. Simon. Scattering Theory for Systems with Different Spatial Asymptotics on the Left and Right. Comm. Math. Phys., 63 : 277–301, 1978. | MR | Zbl

[7] P. Deift, E. Trubowitz. Inverse Scattering on the Line. Comm. Pure Appl. Math., 32 : 121–251, 1979. | MR | Zbl

[8] G. W. Gibbons. Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes. Comm. Math. Phys., 44 : 245–264, 1975. | MR

[9] D. Häfner. Complétude asymptotique pour l’équation des ondes dans une classe d’espaces-temps stationnaires et asymptotiquement plats. Ann. Inst. Fourier (Grenoble), 51 : 779–833, 2001. | Numdam | Zbl

[10] D. Häfner. Sur la théorie de la diffusion pour l’équation de Klein-Gordon dans la métrique de Kerr. Dissertationnes Mathematicae, 421 : 102 pp., 2003. | Zbl

[11] F. Melnyk. Scattering on Reissner-Nordstrøm metric for massive charged spin 1/2 fields. Ann. Henri Poincaré, 4(5) : 813–846, 2003. | MR | Zbl

[12] F. Melnyk. The Hawking effect for spin 1/2 fields. Comm. Math. Phys., 244(3) : 483–525, 2004. | MR | Zbl

[13] J-P. Nicolas. A non linear Klein-Gordon equation on Kerr metrics. J. Math. Pures Appl., 81(9) : 885–203, 2002. | MR | Zbl

[14] J-P. Nicolas. Dirac fields on asymptotically flat space-time. Dissertationnes Mathematicae, 408, 85 pp., 2002. | MR | Zbl

[15] R. Ruffini. The Dyadosphere of black holes and gamma-ray bursts. Astron. Astrophys. Suppl. Ser., 138(3) : 513–514, 1999.

[16] S.N.M. Ruijsenaars, P.J.M. Bongaarts. Scattering theory for one-dimensional step potentials. Ann. Inst. Henri Poincaré, Sec. A, 26(1) : 1–17, 1977. | Numdam | MR | Zbl

[17] S.H. Tang, M. Zworski. Resonance expansions of scattered waves . Comm. Pure and Appl. Math., 53 : 1305–1334, 2000. | MR | Zbl