A rigidity property for a type of wave-Klein-Gordon system

Abstract

In this paper we investigate the rigidity property of a wave component coupled in a wave-Klein-Gordon system. We prove that when the radiation field of the wave component vanishes at the null infinity, the initial data of this component also vanish, therefore there is no wave in the whole spacetime. Introduction.In the present work we establish a rigidity result of the following Cauchy problem 1 of a wave-Klein-Gordon system in R 1+3 :