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

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

2011-10-10

arxiv.org/abs/1110.2009v1

Ann. Henri Poincare 8 (2011), 1491-1538

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, 6 figures; published version of results contained in the second part of arXiv:1006.0283, various new results added;

Scientific paper

This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We here obtain definitive energy and pointwise decay, non-decay and blow-up results. Our estimates hold up to and including the horizon. A hierarchy of conservations laws on degenerate horizons is also derived.

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