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Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I

  • Stefanos AretakisEmail author
Article

Abstract

We study the problem of stability and instability of extreme Reissner-Nordström spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation \({\square_{g}\psi=0}\) on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface Σ0 crossing the future event horizon \({\mathcal{H}^{+}}\) . We obtain boundedness, decay and non-decay results. Our estimates hold up to and including the horizon \({\mathcal{H}^{+}}\) . The fundamental new aspect of this problem is the degeneracy of the redshift on \({\mathcal{H}^{+}}\) . Several new analytical features of degenerate horizons are also presented.

Keywords

Black Hole Wave Equation Event Horizon Linear Stability Extreme Black Hole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUnited Kingdom

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