Linear waves in the interior of extremal black holes I

Abstract

We consider solutions to the linear wave equation in the interior region of extremal Reissner-Nordström black holes. We show that, under suitable assumptions on the initial data, the solutions can be extended continuously beyond the Cauchy horizon and moreover, that their local energy is finite. This result is in contrast with previously established results for subextremal Reissner-Nordström black holes, where the local energy was shown to generically blow up at the Cauchy horizon.

46 pages, 2 figures

References in corpus (10)

• Gravitational instability of an extreme Kerr black hole
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations
• Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
• Linear waves in the interior of extremal black holes I
• Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion
• Boundedness of massless scalar waves on Kerr interior backgrounds
• Late-time decay of perturbations outside extremal charged black hole
• Linear waves in the interior of extremal black holes II

Cited by in corpus (22)

• Analysis of linear waves near the Cauchy horizon of cosmological black holes
• Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• Linear waves in the interior of extremal black holes I
• Rough initial data and the strength of the blue-shift instability on cosmological black holes with $\Lambda >0$
• Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
• The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples
• Horizon hair of extremal black holes and measurements at null infinity
• Boundedness of massless scalar waves on Kerr interior backgrounds
• Generic blow-up results for the wave equation in the interior of a Schwarzschild black hole
• The interior of dynamical extremal black holes in spherical symmetry
• A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordstrom
• The trapping effect on degenerate horizons
• Polynomial Blow-up Upper Bounds for the Einstein-scalar field System Under Spherical Symmetry
• The non-linear stability of the Schwarzschild family of black holes
• Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere
• Asymptotic blow-up for a class of semilinear wave equations on extremal Reissner-Nordström spacetimes
• Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole
• Instability results for the wave equation in the interior of Kerr black holes
• Overdamped quasibound states inside a Schwarzschild black hole
• Strong cosmic censorship for the spherically symmetric Einstein-Maxwell-charged-Klein-Gordon system with positive $\Lambda$: stability of the Cauchy horizon and $H^1$ extensions
• Linear Instability of the Reissner-Nordström Cauchy Horizon