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Superradiance and scattering of the charged Klein–Gordon field by a step-like electrostatic potential

Superradiance and scattering of the charged Klein–Gordon field by a step-like electrostatic potential

Authors :
Bachelot, Alain
Source :
Journal de Mathematiques Pures et Appliquees. Oct2004, Vol. 83 Issue 10, p1179-1239. 61p.
Publication Year :
2004

Abstract

We develop the scattering theory for the charged Klein–Gordon equation on <f>Rt×Rx</f>, when the electrostatic potential <f>A(x)</f> has different asymptotics <f>a±</f> as <f>x→±∞</f>. In this case, the conserved energy is not positive definite (Klein paradox). We construct the spectral representation for the harmonic equation. Since <f>a+≠a-</f>, the distorted Fourier transform has to be defined on weighted <f>L2</f>-spaces, and spectral quantities of a new type can appear, that are neither eigenvalues, nor resonances. These so called “hyperradiant modes” are real singularities of the Green function, and lead to solutions polynomially increasing in time. We investigate the asymptotic behaviours of the solutions as <f>t→±∞</f>, and we establish the existence of a Scattering operator the symbol of which has a norm strictly larger than 1, for the frequencies in <f>(a-,a+)</f>. We apply these results to the DeSitter–Reissner–Nordstrøm metric, to justify rigorously the notion of superradiance of charged black-holes. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
00217824
Volume :
83
Issue :
10
Database :
Academic Search Index
Journal :
Journal de Mathematiques Pures et Appliquees
Publication Type :
Academic Journal
Accession number :
14513877
Full Text :
https://doi.org/10.1016/j.matpur.2004.03.007