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Annales Henri Poincaré

, Volume 12, Issue 8, pp 1491–1538 | Cite as

Stability and Instability of Extreme Reissner–Nordström Black Hole Spacetimes for Linear Scalar Perturbations II

  • Stefanos AretakisEmail author
Article

Abstract

This paper contains the second part of a two-part series on the stability and instability of extreme Reissner–Nordström spacetimes for linear scalar perturbations. We continue our study of 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 here obtain definitive energy and pointwise decay, non-decay and blow-up results. Our estimates hold up to and including the horizon \({\mathcal{H}^{+}}\). A hierarchy of conservations laws on degenerate horizons is also derived.

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 Basel AG 2011

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK

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