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

By S. Aretakis. 2011

223 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c15d8687334a1443ae75cf6ed6ea78cac6c5d0bd

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Citations in the corpus

Numerical methods for finding stationary gravitational solutions (2015, background): “10 Absent from this topical review will be the Aretakis instability [362–368] effecting extreme black holes.”
Black Holes Without Spacelike Singularities (2012, background): “It is slightly amusing that the closer the black hole is to extremality, the more “stable” its Cauchy horizon, when set against the backdrop of the novel instability discovered by Aretakis [1, 2] in his study of the wave equation on exactly extreme Reissner–Nordström; this then suggests that, as th”
Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M (2014, background): “In view of the recently discovered Aretakis instability [8, 9, 7, 47, 53], the precise analogue of the above Theorem does not in fact hold without qualification in the case of extremality ∣a∣ = M .”
Horizon Instability of Extremal Black Holes (2012, unknown): “Furthermore, we note that sharp quantitative estimates have been shown in [2, 3] for each angular frequency l ∈ N.”