The radiation bound for a Klein-Gordon field on a static spherical spacetime

Abstract

We establish a well-posed Cauchy problem in Minkowski (R4, η), associated with a radiating Klein-Gordon field ψ(x) = eztψ(xi), in curvature coordinates {xμ = t, p, θ,Φ} on a static spherically symmetric spacetime (M, g). This is crucial to our primary concern with proving an optimal L2-bound on the radiating field ψ, decaying at asymptotic spatial infinity, and manifests as the content of our main Theorem 1: A proof of the Sommerfeld Finiteness Condition for K-G radiation on (M,g).