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

Abstract

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

33 pages, 6 figures; published version of results contained in the second part of arXiv:1006.0283, various new results added; Ann. Henri Poincare, 2011, online first

References in corpus (12)

• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I
• A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
• The black hole stability problem for linear scalar perturbations
• The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant
• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• The wave equation on Schwarzschild-de Sitter spacetimes
• 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
• A uniqueness theorem for degenerate Kerr-Newman black holes
• Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole
• The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results
• Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry

Cited by in corpus (102)

• Classification of near-horizon geometries of extremal black holes
• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I
• Numerical Methods for Finding Stationary Gravitational Solutions
• Black holes without spacelike singularities
• Gravitational instability of an extreme Kerr black hole
• On the horizon instability of an extreme Reissner-Nordström black hole
• Analysis of linear waves near the Cauchy horizon of cosmological black holes
• Black holes as particle accelerators: a brief review
• Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
• Instability of supersymmetric microstate geometries
• Exploring New Physics Frontiers Through Numerical Relativity
• What happens at the horizon(s) of an extreme black hole?
• Absorption of a massive scalar field by a charged black hole
• A perturbative perspective on self-supporting wormholes
• General classification of charged test particle circular orbits in Reissner--Nordström spacetime
• Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate
• Towards a Non-singular Paradigm of Black Hole Physics
• The excitation of quadratic quasinormal modes for Kerr black holes
• Asymptotics of linear waves and resonances with applications to black holes
• A note on instabilities of extremal black holes under scalar perturbations from afar
• 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
• Spacetime Singularities and Cosmic Censorship Conjecture: A Review with Some Thoughts
• Nonlinear instability of scalar fields on extremal black holes
• Linear waves in the interior of extremal black holes I
• Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
• Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
• High energy collision of two particles in wormhole spacetimes
• Characterisation of the Energy of Gaussian Beams on Lorentzian Manifolds - with Applications to Black Hole Spacetimes
• Quasinormal modes in extremal Reissner-Nordström spacetimes
• Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes
• Mass Ladder Operators from Spacetime Conformal Symmetry
• Horizon hair of extremal black holes and measurements at null infinity
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• The linear stability of Reissner-Nordström spacetime: the full subextremal range
• Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited
• High Energy Collision of Particles in the Vicinity of Extremal Black Holes in Higher Dimensions: Banados-Silk-West Process as Linear Instability of Extremal Black Holes
• Horizon instability of extremal Reissner-Nordström black holes to charged perturbations
• The fate of stringy AdS vacua and the WGC
• Aretakis Charges and Asymptotic Null Infinity
• Instability of higher dimensional extreme black holes
• A model problem for quasinormal ringdown on asymptotically flat or extremal black holes
• Boundedness of massless scalar waves on Kerr interior backgrounds
• Turning black-holes and D-branes inside out their photon-spheres
• Late-time decay of perturbations outside extremal charged black hole
• Is there a breakdown of effective field theory at the horizon of an extremal black hole?
• The weak null condition and global existence using the p-weighted energy method
• A swamp of non-SUSY vacua
• Exotic Holographic Dispersion
• Near-extremal black holes at late times, backreacted
• Price's law and precise late-time asymptotics for subextremal Reissner-Nordström black holes
• A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordstrom
• Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum
• Holographic Response of Electron Clouds
• Particle collision with an arbitrarily high center-of-mass energy near a Bañados-Teitelboim-Zanelli black hole
• On the linear stability of the extreme Kerr black hole under axially symmetric perturbations
• (Transient) Scalar Hair for (Nearly) Extreme Black Holes
• Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails
• Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole
• The trapping effect on degenerate horizons
• Stationary Black Holes as Holographs II
• The $r^p$-weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications
• General relation between Aretakis charge and Newman-Penrose charge
• Extremal Tunneling and Anti-de Sitter Instantons
• General first-order mass ladder operators for Klein-Gordon fields
• A class of conformal curves in the Reissner-Nordström spacetime
• Dynamical AdS strings across horizons
• The wave equation on the extreme Reissner-Nordström black hole
• Charge Loss (or the Lack Thereof) for AdS Black Holes
• On Late Time Tails in an Extreme Reissner-Nordström Black Hole: Frequency Domain Analysis
• A Yang-Mills field on the extremal Reissner-Nordström black hole
• Evanescent ergosurface instability
• Effect of the self-gravity of shells on a high energy collision in a rotating Bañados-Teitelboim-Zanelli spacetime
• Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity
• Evolutions from extremality
• Asymptotic blow-up for a class of semilinear wave equations on extremal Reissner-Nordström spacetimes
• Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere
• Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole
• Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes
• Black Hole as a Wormhole Factory
• Fully extremal black holes: a black hole graveyard?
• Gaussian null coordinates, near-horizon geometry and conserved charges on the horizon of extremal non-dilatonic black $p$-branes
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons
• The characteristic gluing problem for the Einstein equations and applications
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes
• Horizon Instability of the Extremal BTZ Black Hole
• Gaussian Null Coordinates for Rotating Charged Black Holes and Conserved Charges
• Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry
• The global structure of spherically symmetric charged scalar field spacetimes
• Strong cosmic censorship and Misner spacetime
• Localized energy estimates on Myers-Perry space-times
• Pseudospectrum of Reissner-Nordström black holes: quasinormal mode instability and universality
• On the Stability of a Wormhole in the Maximally-Extended Reissner-Nordström Solution
• An Approach to Stability Analyses in General Relativity via Symplectic Geometry
• Non-linear instability of slowly rotating Kerr-AdS black holes
• Decay and non-decay for the massless Vlasov equation on subextremal and extremal Reissner-Nordström black holes
• Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
• Classical Unattainability of Extremality in non-BPS D-brane Systems
• Corrections to the Aretakis type behaviour of the metric due to an infalling particle
• Approaching a dynamical extreme black hole horizon
• A Nonlinear Endpoint of Charged Horizon Instabilities