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

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 square(g)psi = 0 on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface Sigma(0) crossing the future event horizon H(+). We here obtain definitive energy and pointwise decay, non-decay and blow-up results. Our estimates hold up to and including the horizon H(+). A hierarchy of conservations laws on degenerate horizons is also derived.