Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric

DOI10.1142/S0219891621500090zbMath1482.35127arXiv2004.02483OpenAlexW3201504091WikidataQ115245168 ScholiaQ115245168MaRDI QIDQ5018994

Dietrich Häfner, Nicolas Besset

Publication date: 27 December 2021

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02483

zbMATH Keywords

charged Klein-Gordon equationgrowing modesde Sitter-Kerr-Newman metric

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Black holes (83C57) Perturbations in context of PDEs (35B20) PDEs in connection with relativity and gravitational theory (35Q75) Resonance in context of PDEs (35B34) Second-order hyperbolic equations (35L10) Linear higher-order PDEs (35G05) PDEs on manifolds (35R01)

Related Items (3)

Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations ⋮ Recent progress in general relativity ⋮ The Goursat problem at the horizons for the Klein–Gordon equation on the de Sitter–Kerr metric

Cites Work

• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
• Resonances for asymptotically hyperbolic manifolds: Vasy's method revisited
• Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole
• Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric
• The global non-linear stability of the Kerr-de Sitter family of black holes
• Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
• Asymptotic completeness for superradiant Klein-Gordon equations and applications to the de Sitter-Kerr metric
• Decay of the local energy for the charged Klein-Gordon equation in the exterior de Sitter-Reissner-Nordström spacetime
• Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
• Superradiant instabilities for short-range non-negative potentials on Kerr spacetimes and applications
• Linear stability of slowly rotating Kerr black holes
• Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
• Reissner–Nordstrøm–de Sitter manifold: photon sphere and maximal analytic extension

This page was built for publication: Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric