L$^{\infty}$ Decay Estimate for the Klein-Gordon Equation in the Anti-de Sitter Model of the Universe

Abstract

We consider the inital value problem for the Klein-Gordon equation with non-zero initial data in anti-de Sitter spacetime. $L^{\infty}$ decay estimate is derived for the solutions to the linear Klein-Gordon equations in the anti-de Sitter spacetime without source term.