A Note on Wave Equation in Einstein & de Sitter Spacetime

TL;DR

This paper studies wave equations in Einstein & de Sitter spacetime, providing explicit solutions and estimates, advancing understanding of wave behavior in this cosmological model.

Contribution

It introduces the initial value problem for the wave equation in Einstein & de Sitter spacetime and derives explicit solution formulas and $L^p - L^q$ estimates.

Findings

Explicit solution formulas for wave equations in Einstein & de Sitter spacetime

Derivation of $L^p - L^q$ estimates for solutions

Analysis of the non-Fuchsian nature of the differential operator

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.