Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds

DOI10.1016/j.jfa.2012.08.015zbMath1254.83021arXiv1110.2006OpenAlexW2964046786MaRDI QIDQ1760177

Stefanos Aretakis

Publication date: 13 November 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2006

zbMATH Keywords

wave equationextremal black holesKerr black holesstability of black holes

Mathematics Subject Classification ID

Black holes (83C57) Wave equation (35L05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Equations of motion in general relativity and gravitational theory (83C10) Approximation procedures, weak fields in general relativity and gravitational theory (83C25)

Related Items (46)

Linear waves in the interior of extremal black holes. I ⋮ Boundedness of massless scalar waves on Reissner-Nordström interior backgrounds ⋮ Decay for solutions of the wave equation on Kerr exterior spacetimes. III: The full subextremalcase \(|a| < M\). ⋮ On the horizon instability of an extreme Reissner-Nordström black hole ⋮ Critical exponents of extremal Kerr perturbations ⋮ Gravitational waves from plunges into Gargantua ⋮ Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes ⋮ The characteristic gluing problem and conservation laws for the wave equation on null hypersurfaces ⋮ Computing the quasinormal modes and eigenfunctions for the Teukolsky equation using horizon penetrating, hyperboloidally compactified coordinates ⋮ Normally hyperbolic trapping on asymptotically stationary spacetimes ⋮ Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes ⋮ Time-periodic Einstein-Klein-Gordon bifurcations of Kerr ⋮ Linear waves in the interior of extremal black holes. II ⋮ Lux in obscuro: photon orbits of extremal black holes revisited ⋮ Late-time asymptotics for geometric wave equations with inverse-square potentials ⋮ Pointwise decay for the wave equation on nonstationary spacetimes ⋮ Lux in obscuro II: photon orbits of extremal AdS black holes revisited ⋮ Late-time tails and mode coupling of linear waves on Kerr spacetimes ⋮ Recent progress in general relativity ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ A vector field method on the distorted Fourier side and decay for wave equations with potentials ⋮ Nonlinear scalar perturbations of extremal Reissner-Nordström spacetimes ⋮ Semi-local quantum criticality and the instability of extremal planar horizons ⋮ A local energy estimate for wave equations on metrics asymptotically close to Kerr ⋮ A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordström ⋮ Global existence for quasilinear wave equations close to Schwarzschild ⋮ A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes ⋮ Time-translation invariance of scattering maps and blue-shift instabilities on Kerr black hole spacetimes ⋮ Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes ⋮ The trapping effect on degenerate horizons ⋮ Boundedness and decay for the Teukolsky equation on Kerr spacetimes. I: The case \(|a|\ll M\) ⋮ Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II: the exterior of the Black Hole region ⋮ Quantitative mode stability for the wave equation on the Kerr spacetime ⋮ Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole ⋮ Unnamed Item ⋮ A perturbative perspective on self-supporting wormholes ⋮ Boundedness of massless scalar waves on Kerr interior backgrounds ⋮ A sharp version of Price's law for wave decay on asymptotically flat spacetimes ⋮ Logarithmic corrections in the asymptotic expansion for the radiation field along null infinity ⋮ Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes ⋮ Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere ⋮ Decay Properties of Klein-Gordon Fields on Kerr-AdS Spacetimes ⋮ Localized Energy Estimates for Wave Equations on (1+4)-dimensional Myers--Perry Space-times ⋮ Asymptotics of linear waves and resonances with applications to black holes ⋮ The Kerr/CFT correspondence and its extensions ⋮ Classification of near-horizon geometries of extremal black holes

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