The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results

Details The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results

2010-06-02

arxiv.org/abs/1006.0283v2

Mathematics

Analysis of PDEs

117 pages, 26 figures; various improvements and minor corrections

Scientific paper

We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold up to and including the event horizon. The fundamental new aspect of this problem is the degeneracy of the redshift on the event horizon. Several new analytical features of degenerate horizons are also presented.

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