Resonances for asymptotically hyperbolic manifolds: Vasy's method revisited

DOI10.4171/JST/153zbMath1365.58012arXiv1511.03352OpenAlexW2963759808MaRDI QIDQ516587

Maciej Zworski

Publication date: 14 March 2017

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03352

zbMATH Keywords

asymptotically hyperbolic manifoldsscattering resonances

Mathematics Subject Classification ID

Black holes (83C57) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) Wave equation (35L05) Elliptic equations on manifolds, general theory (58J05) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Resonance in context of PDEs (35B34) Propagation of singularities; initial value problems on manifolds (58J47) PDEs on manifolds (35R01)

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Quasinormal modes of small Schwarzschild–de Sitter black holes ⋮ Remarks on Vasy’s operator with analytic coefficients ⋮ A global definition of quasinormal modes for Kerr–AdS black holes ⋮ Spectral gaps, additive energy, and a fractal uncertainty principle ⋮ Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes ⋮ Stability of Minkowski space and polyhomogeneity of the metric ⋮ Resonances for symmetric tensors on asymptotically hyperbolic spaces ⋮ Linear stability of slowly rotating Kerr black holes ⋮ Elliptic parametrices in the 0-calculus of Mazzeo and Melrose ⋮ Analysis of linear waves near the Cauchy horizon of cosmological black holes ⋮ The null-geodesic flow near horizons ⋮ Resonances for obstacles in hyperbolic space ⋮ Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes ⋮ A quantitative version of Hawking radiation ⋮ Mathematical study of scattering resonances ⋮ Black hole gluing in de Sitter space ⋮ A sharp version of Price's law for wave decay on asymptotically flat spacetimes ⋮ Microlocal analysis of forced waves ⋮ Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric

Cites Work

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• Stochastic stability of Pollicott–Ruelle resonances
• Asymptotics of radiation fields in asymptotically Minkowski space
• Spectral Theory and Eisenstein Series for Kleinian Groups
• Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets

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