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


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.


Black Hole Wave Equation Event Horizon Linear Stability Extreme Black Hole 
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© Springer Basel AG 2011

Authors and Affiliations

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

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