Abstract
We study a non-local ghost-free Lorentz invariant modification of the Maxwell equations in four- and higher-dimensional flat spacetimes. We construct solutions of these equations for stationary charged and magnetized objects and use them to find the field created by such objects moving with the speed of light.
Highlights
An electric field of a point charge is spherically symmetric and its equipotential surfaces are spheres
Bonnor [3] obtained a similar solution for a spinning gravitating object. These results were later generalized to higher dimensions [4,5,6]. These so-called gyraton metrics are exact solutions of the higher-dimensional Einstein equations and they belong to the class of Kundt metrics [7]
Linearized versions of the gyraton metrics can be obtained by boosting a stationary solution of the linearized Einstein equations for a spinning massive object [8]
Summary
An electric field of a point charge is spherically symmetric and its equipotential surfaces are spheres. A similar effect is well known in gravity: the Aichelburg-Sexl solution [2] of the Einstein equations for an ultrarelativistic gravitating object is of the form of a so-called pp wave. Bonnor [3] obtained a similar solution for a spinning gravitating object. These results were later generalized to higher dimensions [4,5,6]. Linearized solutions of the nonlocal ghost-free equations for stationary objects were derived and discussed in many publications The gravitational field of four-dimensional and higher-dimensional ultrarelativistic massive and spinning objects in linearized nonlocal gravity was found and discussed in a recent work [14]; see Ref.
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