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

Abstract

We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider 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 obtain boundedness, decay and non-decay results. Our estimates hold up to and including the 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.

37 pages, 11 figures; published version of results contained in the first part of arXiv:1006.0283, various new results added

References in corpus (14)

• 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
• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• Improved decay for solutions to the linear wave equation on a Schwarzschild black hole
• 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
• 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 (125)

• Challenges for $\Lambda$CDM: An update
• Classification of near-horizon geometries of extremal black holes
• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II
• 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
• A massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability
• Nonlinear interactions between black holes and Proca fields
• 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?
• Instability of D-dimensional extremally charged Reissner-Nordstrom(-de Sitter) black holes: Extrapolation to arbitrary D
• Quasinormal modes of extremal black holes
• A perturbative perspective on self-supporting wormholes
• General classification of charged test particle circular orbits in Reissner--Nordström spacetime
• Towards a Non-singular Paradigm of Black Hole Physics
• Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate
• Asymptotics of linear waves and resonances with applications to black holes
• The excitation of quadratic quasinormal modes for Kerr black holes
• Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
• 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
• 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
• Almost all extremal black holes in AdS are singular
• High energy collision of two particles in wormhole spacetimes
• Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
• Subleading BMS charges and fake news near null infinity
• Decay of linear waves on higher dimensional Schwarzschild black holes
• Characterisation of the Energy of Gaussian Beams on Lorentzian Manifolds - with Applications to Black Hole Spacetimes
• From regular black holes to horizonless objects: quasi-normal modes, instabilities and spectroscopy
• Quasinormal modes in extremal Reissner-Nordström spacetimes
• Mass Ladder Operators from Spacetime Conformal Symmetry
• Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes
• Horizon hair of extremal black holes and measurements at null infinity
• The linear stability of Reissner-Nordström spacetime: the full subextremal range
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• 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
• Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies
• Bounded energy waves on the black hole interior of Reissner-Nordström-de Sitter
• Aretakis Charges and Asymptotic Null Infinity
• Long Lived Quasinormal Modes of Regular and Extreme Black Holes
• Instability of higher dimensional extreme black holes
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• A model problem for quasinormal ringdown on asymptotically flat or extremal black holes
• Turning black-holes and D-branes inside out their photon-spheres
• Boundedness of massless scalar waves on Kerr interior backgrounds
• Late-time decay of perturbations outside extremal charged black hole
• Instabilities of extremal rotating black holes in higher dimensions
• Is there a breakdown of effective field theory at the horizon of an extremal black hole?
• A swamp of non-SUSY vacua
• Exotic Holographic Dispersion
• Price's law and precise late-time asymptotics for subextremal Reissner-Nordström black holes
• Near-extremal black holes at late times, backreacted
• A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordstrom
• The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results
• Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum
• Holographic Response of Electron Clouds
• Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails
• On the linear stability of the extreme Kerr black hole under axially symmetric perturbations
• Particle collision with an arbitrarily high center-of-mass energy near a Bañados-Teitelboim-Zanelli black hole
• Late-time tails in extremal Reissner-Nordstrom spacetime
• (Transient) Scalar Hair for (Nearly) Extreme Black Holes
• Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole
• Stationary Black Holes as Holographs II
• The trapping effect on degenerate horizons
• A class of conformal curves in the Reissner-Nordström spacetime
• Extremal Tunneling and Anti-de Sitter Instantons
• General relation between Aretakis charge and Newman-Penrose charge
• General first-order mass ladder operators for Klein-Gordon fields
• The wave equation on the extreme Reissner-Nordström black hole
• Charge Loss (or the Lack Thereof) for AdS Black Holes
• Circumventing Quantum Gravity: Black Holes Evaporating into Macroscopic Wormholes
• 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
• Dynamical AdS strings across horizons
• Massive vector field perturbations on extremal and near-extremal static black holes
• Effect of the self-gravity of shells on a high energy collision in a rotating Bañados-Teitelboim-Zanelli spacetime
• Evolutions from extremality
• Morawetz estimates without relative degeneration and exponential decay on Schwarzschild-de Sitter spacetimes
• Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity
• Massive tensor field perturbations on extremal and near-extremal static 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
• Hairy black holes in N=2 gauged supergravity
• Black Hole as a Wormhole Factory
• Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes
• Gaussian null coordinates, near-horizon geometry and conserved charges on the horizon of extremal non-dilatonic black $p$-branes
• Fully extremal black holes: a black hole graveyard?
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• The characteristic gluing problem for the Einstein equations and applications
• Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons
• Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes
• Generalised hyperbolicity in spacetimes with string-like singularities
• Small deformations of extreme five dimensional Myers-Perry black hole initial data
• 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
• Localized energy estimates on Myers-Perry space-times
• On the conformal structure of the extremal Reissner-Nordström spacetime
• 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
• Pseudospectrum of Reissner-Nordström black holes: quasinormal mode instability and universality
• Strong cosmic censorship and Misner spacetime
• Non-linear instability of slowly rotating Kerr-AdS black holes
• Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
• On the Stability of a Wormhole in the Maximally-Extended Reissner-Nordström Solution
• Relatively non-degenerate integrated decay estimates for massless Vlasov fields on Schwarzschild spacetimes
• Charged Scalar Field at Future Null Infinity via Nonlinear Hyperboloidal Evolution
• Classical Unattainability of Extremality in non-BPS D-brane Systems
• Decay and non-decay for the massless Vlasov equation on subextremal and extremal Reissner-Nordström black holes
• An Approach to Stability Analyses in General Relativity via Symplectic Geometry
• Approaching a dynamical extreme black hole horizon
• Corrections to the Aretakis type behaviour of the metric due to an infalling particle
• A Nonlinear Endpoint of Charged Horizon Instabilities
• Bounds for the metric and shift vector on extreme Kerr under linear axially symmetric gravitational perturbations