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

By S. Aretakis. 2011

175 citations recorded by the source corpus.

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.

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

View Paper: https://www.semanticscholar.org/paper/37069ff19d99db406a025c1ac9f87705300901e3

Citations in the corpus

• Horizon Instability of Extremal Black Holes (2012, unknown): “Combining the methods of [3], the results of the present paper (note, in particular, that the condition (13) holds on extremal Kerr) and [4] and by projecting to the zeroth azimuthal frequency we obtain the following”