A nonlinear Klein--Gordon equation on Kerr metrics

DOI10.1016/S0021-7824(02)01272-2zbMath1029.83029OpenAlexW2087441264MaRDI QIDQ1406916

Jean-Philippe Nicolas

Publication date: 7 September 2003

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-7824(02)01272-2

zbMATH Keywords

nonlinear partial differential equationsblack holesgeneral relativity

Mathematics Subject Classification ID

Black holes (83C57) Second-order nonlinear hyperbolic equations (35L70) Exact solutions to problems in general relativity and gravitational theory (83C15)

Related Items (15)

Local Cauchy problem for the nonlinear Dirac and Dirac-Klein-Gordon equations on Kerr space–time ⋮ Klein paradox for the charged Klein-Gordon equation: superradiance and scattering. ⋮ SCATTERING OF MASSLESS DIRAC FIELDS BY A KERR BLACK HOLE ⋮ A large data theory for nonlinear wave on the Schwarzschild background ⋮ Conformal scattering theory for the Dirac equation on Kerr spacetime ⋮ Peeling of Dirac field on Kerr spacetime ⋮ Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime ⋮ Blow-up and lifespan estimate to a nonlinear wave equation in Schwarzschild spacetime ⋮ A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds ⋮ Propagation of massive scalar fields in pre-big bang cosmologies ⋮ Superradiance and scattering of the charged Klein-Gordon field by a step-like electrostatic potential ⋮ Peeling on Kerr spacetime: linear and semi-linear scalar fields ⋮ On global hyperbolicity of spacetimes: some recent advances and open problems ⋮ Small-amplitude nonlinear waves on a black hole background ⋮ An integral spectral representation of the propagator for the wave equation in the Kerr geometry

Cites Work

• Solution globale d'une équation non linéaire sur une variété hyperbolique
• Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric. I
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• Nonlinear Klein-Gordon equation on Schwarzschild-like metrics
• Diffusion d'un champ massif et chargé de Dirac en métrique de Reissner–Nordstrøm
• Global exterior cauchy problem for spin 3/2 zero rero-mass fields in the schwarzschild space-time
• Nonlinear Dirac fields on the Schwarzschild metric
• Scattering of massive Dirac fields on the Schwarzschild black hole spacetime
• Dirac fields on asymptotically flat space-times
• The Evolution of the Weyl and Maxwell Fields in Curved Space—Times
• Zero rest-mass fields including gravitation: asymptotic behaviour
• General Relativity
• Creation of fermions at the charged black-hole horizon
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