Asymptotic behaviour of Maxwell fields in higher dimensions

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.Comment: 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 correcte

Electromagnetic fields with vanishing quantum corrections

We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.Comment: 7 pages. v2: presentation of the type III conditions improved, discussion extended, new ref

Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class

We study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n>=4 dimensions. As it turns out, the character of these exact solutions depends significantly on the (relative) value of n and p. In odd dimensions the solutions reduce to static black holes dressed by an electric and a magnetic field and whose horizon is an Einstein space (further constrained by the Einstein-Maxwell equations) -- both the Weyl and Maxwell type are D. Even dimensions, however, open up more possibilities. In particular, when 2p=n there exist non-static solutions describing black holes acquiring (or losing) mass by receiving (or emitting) electromagnetic radiation. In this case the Weyl type is II (D) and the Maxwell type can be II (D) or N. Conditions under which the Maxwell field is self-dual (for odd p) are also discussed, and a few explicit examples presented. Finally, the case p=1 is special in all dimensions and leads to static metrics with a non-Einstein transverse space.Comment: 34 pages. v2: improved discussion following eq. (84), references updated, minor changes to match the published versio