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

TL;DR

This paper proves a rigidity property for a wave-Klein-Gordon system, showing that if the wave component's radiation field vanishes at null infinity, then the entire wave component must be zero throughout spacetime.

Contribution

It establishes a new rigidity result linking the vanishing radiation field at null infinity to the triviality of the wave component in the system.

Findings

Vanishing radiation field implies zero wave component in the entire spacetime.

The result applies specifically to coupled wave-Klein-Gordon systems.

Provides insight into the asymptotic behavior of solutions at null infinity.

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, therefor there is no wave in the whole spacetime