Stability and Instability of Extreme Reissner-Nordstr'om Black Hole Spacetimes for Linear Scalar Perturbations II

摘要

This paper contains the second part of a two-part series on the stability andinstability of extreme Reissner-Nordstrom spacetimes for linear scalarperturbations. We continue our study of solutions to the linear wave equationon a suitable globally hyperbolic subset of such a spacetime, arising fromregular initial data prescribed on a Cauchy hypersurface crossing the futureevent horizon. We here obtain definitive energy and pointwise decay, non-decayand blow-up results. Our estimates hold up to and including the horizon. Ahierarchy of conservations laws on degenerate horizons is also derived.