Nonlinear perturbations of Reissner-Nordström black holes

Abstract

We develop a nonlinear perturbation theory of Reissner-Nordström 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.

arXiv comment9 pages

References in corpus (9)

• On weakly turbulent instability of anti-de Sitter space
• Master equations for perturbations of generalised static black holes with charge in higher dimensions
• Quasinormal modes and Strong Cosmic Censorship
• Gravitational radiation from Schwarzschild black holes: the second order perturbation formalism
• Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
• Strong cosmic censorship: taking the rough with the smooth
• A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
• Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes
• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum

Cited by in corpus (2)

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