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

Abstract

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.

117 pages, 26 figures; various improvements and minor corrections

References in corpus (12)

• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I
• The black hole stability problem for linear scalar perturbations
• A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant
• The wave equation on Schwarzschild-de Sitter spacetimes
• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• A note on energy currents and decay for the wave equation on a Schwarzschild background
• Decay Rates for Spherical Scalar Waves in the Schwarzschild Geometry
• Local energy estimate on Kerr black hole backgrounds
• Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole
• Local decay of waves on asymptotically flat stationary space-times

Cited by in corpus (8)

• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I
• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II
• A note on instabilities of extremal black holes under scalar perturbations from afar
• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• Linear waves in the interior of extremal black holes I
• On the quasilinear wave equations in time dependent inhomogeneous media
• A class of conformal curves in the Reissner-Nordström spacetime
• The wave equation on the extreme Reissner-Nordström black hole