Gravitational Radiation Coupled to a real massive scalar Field
Yue Ma, Xianghao Wu, Weidong Zhang
Abstract
We study the asymptotic behavior of small-data global solutions to the Einstein--Klein--Gordon system with a positive-mass real scalar field in wave gauge. We show that the linearized trace component of the metric perturbation admits a t-1 t-1 optimal decreasing rate. Moreover, a quantitative one-point observability estimate is established: the initial Klein-Gordon energy is controlled by this leading order coefficient.
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