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

  • Stefanos AretakisEmail author


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.


Black Hole Wave Equation Event Horizon Linear Stability Extreme Black Hole 
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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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