Asymptotic behaviour of Maxwell fields in higher 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.

23 pages. v2: new appendix A summarizes the definitions of the Ricci rotation coefficients; several technical details moved to new appendix B; former footnote 8 was not precise and has been removed; added/fixed references, typos corrected

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Cited by in corpus (3)

• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Asymptotic properties of gravitational and electromagnetic fields in higher dimensions