Scalar Wave Tails in Even Dimensional Weakly Curved Static Newtonian Spacetimes

In a 4-dimensional (4D) weak field geometry governed by the linearized Einstein's equations and sourced primarily by a static, spatially localized, but otherwise arbitrary mass density $T_{00}$, it is known that the leading order tail part of the Green's functions of the minimally coupled massless scalar, Lorenz gauge photon, and de Donder gauge graviton at late times are not only time translation symmetric, but also space-translation and spherically symmetric. Only the monopole moment of the matter source is responsible for the late-time tail of the Green's functions. We provide evidence, in this paper, that both of these statements will cease to hold for all even dimensions higher than 4. As a consequence, we anticipate that the late time behavior of massless fields propagating in higher even dimensional asymptotically flat spacetimes will exhibit richer phenomenology than their 4D counterparts.