Asymptotic behaviour of Maxwell fields in higher dimensions

TL;DR

This paper investigates how electromagnetic fields decay at infinity in higher-dimensional Einstein spacetimes, revealing different fall-off behaviors and peeling properties that differ from four-dimensional cases, with special cases in even dimensions.

Contribution

It characterizes the asymptotic fall-off and peeling behavior of Maxwell fields in higher dimensions, including special cases in even dimensions and the influence of boundary conditions.

Findings

Different boundary conditions lead to various fall-off rates.

Radiative fields exhibit a peeling behavior distinct from four-dimensional cases.

Special properties occur for p=n/2 in even dimensions.

Abstract

We study the fall-off behaviour of test electromagnetic fields in higher dimensions as one approaches infinity along a congruence of "expanding" null geodesics. The considered backgrounds are Einstein spacetimes including, in particular, (asymptotically) flat and (anti-)de Sitter spacetimes. Various possible boundary conditions result in different characteristic fall-offs, in which the leading component can be of any algebraic type (N, II or G). In particular, the peeling-off of radiative fields F=Nr^{1-n/2}+Gr^{-n/2}+... differs from the standard four-dimensional one (instead it qualitatively resembles the recently determined behaviour of the Weyl tensor in higher dimensions). General p-form fields are also briefly discussed. In even n dimensions, the special case p=n/2 displays unique properties and peels off in the "standard way" as F=Nr^{1-n/2}+IIr^{-n/2}+.... A few explicit examples are mentioned.