Huygens' principle for the Klein-Gordon equation in the de Sitter spacetime

DOI10.1063/1.4821115zbMath1284.81125arXiv1206.0239OpenAlexW3102274895MaRDI QIDQ5409680

Karen Yagdjian

Publication date: 14 April 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0239

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (18)

On a semilinear wave equation in anti-de Sitter spacetime: The critical case ⋮ Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes ⋮ The maximum principle and sign changing solutions of the hyperbolic equation with the Higgs potential ⋮ Global in time existence of self-interacting scalar field in de Sitter spacetimes ⋮ A dissipation-preserving scheme to approximate radially symmetric solutions of the Higgs boson equation in the de Sitter space-time ⋮ Remarks on the derivation of several second order partial differential equations from a generalization of the Einstein equations ⋮ On the initial value problem for the wave equation in Friedmann–Robertson–Walker space–times ⋮ A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes ⋮ Huygens' principle for the Dirac equation in spacetime of non-constant curvature ⋮ Integral Transform Approach to Time-Dependent Partial Differential Equations ⋮ Global existence of the self-interacting scalar field in the de Sitter universe ⋮ Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime ⋮ Integral transform approach to solving Klein-Gordon equation with variable coefficients ⋮ An implicit and convergent method for radially symmetric solutions of Higgs' boson equation in the de Sitter space-time ⋮ A novel integral transform approach to solving hyperbolic equations in the curved space-times ⋮ Huygens’ principle for the generalized Dirac operator in curved spacetime ⋮ The 𝒫(𝜑)₂ Model on de Sitter Space ⋮ Asymptotic behaviors of global solutions for a semilinear diffusion equation in the de Sitter spacetime

Cites Work

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• Huygens' principle and Hadamard's conjecture
• The semilinear Klein-Gordon equation in de Sitter spacetime
• A parametrix for the fundamental solution of the Klein-Gordon equation on asymptotically de Sitter spaces
• The wave equation on asymptotically de Sitter-like spaces
• Hierarchies of Huygens' operators and Hadamard's conjecture
• Lacunas for hyperbolic differential operators with constant coefficients. II
• MASSIVE GRAVITY ON CURVED BACKGROUND
• Fundamental Solutions for Hyperbolic Operators with Variable Coefficients
• Quantum Field Theory in Curved Spacetime
• The hierarchy of Huygens equations in spaces with a non-trivial conformal group
• On the Global Solutions of the Higgs Boson Equation
• Late-time tails in the Kerr spacetime
• Champs spinoriels et propagateurs en relativité générale
• The Large Scale Structure of Space-Time
• Quantum Fields in Curved Space
• Stability of massive cosmological gravitons

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