A Note on Wave Equation in Einstein & de Sitter Spacetime

Abstract

We consider the wave propagating in the Einstein & de Sitter spacetime. The covariant d'Alembert's operator in the Einstein & de Sitter spacetime belongs to the family of the non-Fuchsian partial differential operators. We introduce the initial value problem for this equation and give the explicit representation formulas for the solutions. We also show the $L^p-L^q$ estimates for solutions.

References in corpus (3)

• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• Black hole formation from massive scalar field collapse in the Einstein-de Sitter universe
• Quasi-self-similar evolution of the two-point correlation function: strongly nonlinear regime in Omega_0 < 1 universes

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• Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
• The mode solution of the wave equation in Kasner spacetimes and redshift
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• Solutions of the wave equation bounded at the Big Bang
• Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes
• Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case