Abstract. We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a local energy decay estimate, we prove that sufficiently regular solutions to this equation have bounded conformal energy. As an application we also show a conformal energy estimate with vector fields applied to the solution as well as a global L ∞ decay bound in terms of a weighted norm on initial data. For solutions to the wave equation in these dynamical backgrounds, our results reduce the problem of establishing the classical pointwise decay rate t −3/2 in the interior and t −1 along outgoing null cones to simply proving that local energy decay holds.

We develop a commuting vector field method for a general class of radiating spacetimes. The metrics we consider include those constructed from global stability problems in general relativity, and our method provides sharp peeling estimates for solutions to both linear and (null form) nonlinear scalar fields.

Hi! My name is Fadi Castronovo, I am an Assistant Professor of Engineering at Cal State East Bay. I received my doctorate in Architectural Engineering at Penn State with a minor in Educational Psychology. I am strongly focused on my teaching and research. In my teaching, I strive to provide an engaging and active learning experience to my students, by applying innovative technology and researched pedagogical interventions. I translate this passion for pedagogy in my research by evaluating the intersection of innovative technology and learning.

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