Nonlinear perturbations of Reissner-Nordström black holes

We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to R...

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Bibliographic Details
Published inarXiv.org
Main Author Rutkowski, Mieszko
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.05.2019
Subjects
Black holes
Mathematical analysis
Maxwell's equations
Perturbation theory
Wave equations
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Summary:We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to Regge-Wheeler and Zerilli equations with source and additional coupling to the electromagnetic sector. We construct solutions to the inhomogeneous part of wave equations in terms of sources for Einstein-Maxwell equations. We discuss \(\ell=0\) and \( \ell=1\) cases separately.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.05516