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The Wave Equation on Extreme Reissner-Nordstr\"om Black Hole Spacetimes: Stability and Instability Results

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arxiv 1006.0283 v2 pith:OZN3B42H submitted 2010-06-02 math.AP gr-qcmath-phmath.DGmath.MP

Stefanos Aretakis This is my paper
classification math.APgr-qcmath-phmath.DGmath.MP
keywords eventhorizonequationextremeresultswaveanalyticalarising
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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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