Instability of higher dimensional extreme black holes

Abstract

We study linearized gravitational perturbations of extreme black hole solutions of the vacuum Einstein equation in any number of dimensions. We find that the equations governing such perturbations can be decoupled at the future event horizon. Using these equations, we show that transverse derivatives of certain gauge invariant quantities blow up at late time along the horizon if the black hole solution satisfies certain conditions. We find that these conditions are indeed satisfied by many extreme Myers-Perry solutions, including all such solutions in five dimensions.

19 pages

References in corpus (12)

• Near-horizon symmetries of extremal black holes
• General Kerr-NUT-AdS Metrics in All Dimensions
• 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 classification of near-horizon geometries of extremal vacuum black holes
• Extremal vacuum black holes in higher dimensions
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
• Stability of Five-dimensional Myers-Perry Black Holes with Equal Angular Momenta
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Kerr-NUT-de Sitter Curvature in All Dimensions
• Perturbations of higher-dimensional spacetimes

Cited by in corpus (21)

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• Nonlinear instability of scalar fields on extremal black holes
• Horizon hair of extremal black holes and measurements at null infinity
• 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
• Aretakis Charges and Asymptotic Null Infinity
• How Do Spherical Black Holes Grow Monopole Hair?
• Particle collision with an arbitrarily high center-of-mass energy near a Bañados-Teitelboim-Zanelli black hole
• The trapping effect on degenerate horizons
• Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole
• General relation between Aretakis charge and Newman-Penrose charge
• Effect of the self-gravity of shells on a high energy collision in a rotating Bañados-Teitelboim-Zanelli spacetime
• The Upper Bound of Radiation Energy in the Myers-Perry Black Hole Collision
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• Dilaton Field Released under Collision of Dilatonic Black Holes with Gauss-Bonnet Term
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes
• Spin Interaction under the Collision of Two Kerr-(anti-)de Sitter Black Holes
• Approaching a dynamical extreme black hole horizon