Asymptotic behavior of Maxwell fields in higher dimensions

Abstract

We study the falloff behavior 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 falloffs, in which the leading component can be of any algebraic type (N, II, or G). In particular, the peeling-off of radiative fields $F=N{r}^{1\ensuremath{-}n/2}+G{r}^{\ensuremath{-}n/2}+\dots{}$ differs from the standard four-dimensional one (instead, it qualitatively resembles the recently determined behavior 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 $F=N{r}^{1\ensuremath{-}n/2}+II{r}^{\ensuremath{-}n/2}+\dots{}$. A few explicit examples are mentioned.