Scalar Wave Tails in Even Dimensional Weakly Curved Static Newtonian Spacetimes

TL;DR

This paper investigates how the late-time behavior of massless fields in higher even-dimensional weakly curved static spacetimes differs from the well-understood 4D case, revealing more complex tail phenomena.

Contribution

It provides evidence that the symmetry and monopole dominance of late-time tails in 4D do not hold in higher even dimensions, indicating richer late-time dynamics.

Findings

Late-time tails in higher even dimensions lack symmetry properties.

Monopole moment influence diminishes in higher dimensions.

Higher dimensions exhibit more complex tail behavior.

Abstract

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.